Having given this some thought, it's a bit of a monster question with a few variables that you don't mention. Planetary tilt, which causes seasons is one. Length of day, for example, a rotation like Venus' 116 days would be quite different than an earth rotation of 24 hours and a tidally locked planet would also be different. Atmospheric pressure is another. I'm assuming Earth like tilt, 24 hour day since you didn't mention, and 1 ATM, but I think, if and when we finally get a good look at earth-like exo-planets, which, granted, might be several decades away, I think we'll see a few unexpected things.
OK, moving on. Earth likely got much of it's atmosphere from comets which suggests healthy amounts of CO2, CH4 and NH3, maybe N2, some from the NO family, maybe some Helium, Argon and Neon, those 3 I think we can mostly ignore, some hydrogen perhaps from solar flares, which might get stripped along with the helium from the planet over time.
The total amount of comet and asteroid impacts and ratio of gasses add some variability and a really important factor is whether or not the planet has life and undergoes photosynthesis. Photosynthesis would put O2 into the atmosphere and reduce CO2 and would also have the effect of, over time, reacting with and eliminating the virtually all of the CH4 from the air and any dissolved Iron in the oceans, turning the oceans from a muddy brownish/red to clear blue. Photosynthesis likely played a key role in turning the Earth from a hot planet to a snowball.
So, lots of variables, but it's a fun speculative question, so I'll give it a shot.
How much smaller than Earth? I'm going to go with Venus size but if you have different in mind, let me know. .815 Earth masses, 6,052 km in Radius and gravity of .905 of Earth. Source.
10 miles deep oceans (16.09 km), surface area, 4 Pi R^2 about 7.4 billion cubic km of water. (Earth, by comparison, about 1.37 billion cubic km) Source. Your planet has about 5.4 times as much water as earth (not counting water in the crust, but you didn't mention that, so lets not go there) - and planet size doesn't affect the predictions much.
I wonder how much outgassed CO2 etc. would stay dissolved in the ocean
and how much would accumulate in the atmosphere? Nitrogen?
I'm going to assume that the theory is correct that Earth (and your water world) get most of it's atmosphere and water from asteroids and comets Source and Source, though the 2nd source suggests some could have come from the primordial material of the Earth. If your water-world has a lot of gas trapped below it's crust in it's primordial material, then out-gassing from volcanism becomes a bigger factor and the volcanoes, not the atmosphere above would keep the oceans saturated with gas. That's possible, but I'm going to assume that most of the gas is already in the atmosphere following a late heavy bombardment period. I'll touch a bit more on tectonics later.
Titan Probably got it's thick atmosphere from outgassing Source and perhaps Venus from a recent large outgassing event too - just throwing that out there.
I'm also assuming that your planet wouldn't have permanent ice over it's oceanic poles due to the warmish temperature you implied and likely oceanic circulation not blocked by land-masses would prevent ice formation.
Would it necessarily have a runaway greenhouse?
Greenhouse Gases, CO2, CH4, NO family, (H20, more indirectly)
If your planet has a lot of CO2/CH4, comparable amounts to the amount of H20, then it's unlikely the oceans could begin to dissolve enough gas and this would lead to a run-away Greenhouse, almost without question.
If your planet has more earth like CO2/CH4 levels, perhaps driven by photosynthesis capturing carbon and released oxygen chemically reacting with the CH4, then the runaway greenhouse can be avoided and CH4 be very low concentration. CH4 on Earth is currently about 1.8 PPM and prior to farming and livestock and oil drilling & Fracking which can release some CH4, it was probably less than half that much, less than 1 PPM. In a water world CH4 would probably be even less as there's no biodegrading or digestion of plant-mass releasing CH4.
CO2 is more complicated and the amount dissolved in the ocean depends on the total amount available. If there's not too much CO2 to saturate the oceans, then you have an ocean/air equilibrium which is also affected by temperature. For a more detailed answer on this, look into Henry's law, but I'm going to cheat and do a quick and dirty calculation rather than use Henry's.
on Earth, the oceans contain about 50 times the CO2 as the Atmosphere: Source. And the oceans weigh about 265-270 times more than the atmosphere. (ocean mass given above, atmosphere mass here.)
So if we estimate this as parts per million (ppm), the CO2 concentration in Earth's atmosphere is about 5 times the concentration in Earth's oceans, and at higher temperatures, that ratio goes up, lower temperatures it goes down, but it never gets to the point that there's no CO2 in the air, cause not possible in an equilibrium. With 10 mile deep oceans, we can assume a more CO2 in the oceans, maybe 99% vs about 98% ocean to air ratio currently on earth but the 1% in the air would depend on the total mass of CO2 in the water world's ecosystem, ignoring anything permanently trapped deep on the ocean floor, such as sea-shells.
Would such a world without land always be covered with clouds?
Lets say you have an Earth like Oxygen/Nitrogen atmosphere, 1 bar, a planet very similar to earth but just oceans. Similar weather (as a starting point), this planet should have more clouds as clouds are more common over the oceans, source, and you would have no low humidity/dry pockets of land, but I would think, probably not 100% clouds, just more clouds. The cloud effect on temperature has some uncertainty to it, as clouds both both reflect sunlight making the planet colder during the day and they trap heat at night, so they play for both the warming team and the cooling team, but what I've read, the overall effect is pretty small. Days could be colder, nights warmer.
Also, evaporation tends to cool the air at the surface, which is why islands surrounded by ocean don't ever get the scorching hot temperatures you get in death valley for example, even if they're closer to the equator, so you wouldn't get heatwaves, but you wouldn't get freezing cold either. (I would think).
Finally, oceans have lower albedo and a water-world earth would likely have no ice-caps, so, Overall, I think it's likely a water-world earth would be warmer primarily due to lower albedo and this would increase atmospheric water-vapor (not clouds but transparent water vapor, which is a greenhouse gas), so a water-earth would probably several degrees warmer on average with no ice-caps. How much warmer - I have no idea but I don't think a water-earth would be run-away greenhouse.
A water world (Earth) could also have less CO2 in the atmosphere due to more dissolved in water and probably less CH4 from decaying matter on land, so, it might actually be colder, but this would more likely depend on the life cycle's O2 to CO2 ratio rather than oceanic absorption of CO2. Too many unknowns to say for sure.
Another curious effect to a water world earth is you might get some hurricanes that last for weeks, maybe even months or years in the right conditions, kind of like mini versions of Jupiter's great red spot. All you need for a hurricane to gain strength is warm water and cold air and with no land for the Hurricane to lose strength on, You could get some real jumbos. Maybe category 7s, perhaps 8s. That would be awesome.
Now if (and I think this is the gist of your question), what happens if you decrease the atmospheric pressure by significantly lowering the amount of O2/N2 in the atmosphere (or raising it). Lower atmospheric pressure lowers the boiling point of water and if you lower the atmospheric pressure enough, then water starts to boil and you get a partial water vapor atmosphere as a result of low atmospheric pressure and lots of water. I suspect this is unlikely to actually happen as a planet should always have enough other types of gas to prevent this unlikely outcome but a water vapor atmosphere can be approached logically, even if it's not going to really happen. Now, this isn't just high humidity, this is an actual water vapor atmosphere.
I imagine a water-vapor rich atmosphere would form droplets and rain fairly regularly and be permanent or nearly permanent cloud cover but that's just a guess, though it would probably appear more like low to the ground smog than cloud cover, the clouds might hover much closer to the earth.
If you increase atmospheric pressure, then water has a higher boiling point and takes more energy to vaporize. A denser atmosphere might hold heat better and be a bit warmer. It might also have fewer clouds due to more air and perhaps less variation in temperature and circulation, as it's circulation and warm air cooling off that's the primary driver in cloud formation.
Water vapor would still form under a higher pressure atmosphere by wind and by photons. Sunlight plays an important role in evaporation, perhaps even more than temperature based on pan evaporation studies.
If you have a very thin atmosphere made almost entirely of water (getting back to our improbable example). You'd drown if you tried to breath it, but as far as temperature of such a planet, at least with earth temperatures, water stays liquid even at quite quite low atmospheric pressure.
At 1/2 PSI (1/29th of 1 atm) the boiling temperature of water is 79.6 degrees C. Source. I'm not sure how much heat 1/29th of an atmosphere could trap even if it was mostly water which is a greenhouse gas, so this one is hard to predict. You'd likely see wild night to daytime temperature swings, frequent boiling of the oceans during the day and very heavy rainfall at night, much more rain than we ever see on earth, as 1/29th of an ATM of water vapor is several times more water than is in the earth's atmosphere at any given time.
If a water-vapor atmosphere planet (unlikely), got enough heat from it's sun, it could certainly turn into a run-away greenhouse, but I'm not sure if that happens at the radiance earth gets. But a planet like this would probably be subject to bigger temperature swings than we see on Earth and very fast wind.
How about such a world with no vulcanism?
(Vulcanism - as in, spock, . . . sorry).
We think of plate tectonics and volcanism as a process by which gas is given to the atmosphere, and that's true to an extent. Certainly any gas trapped inside a planet at formation can be outgassed through Volcanism, but perhaps a more important aspect of plate tectonics isn't the release of gas but the absorption of gas. Oxygen is very reactive and it combines with basaltic rock to make lighter/stronger rock like granite and bedrock which leads to continents and mountain ranges and all that good stuff. Nitrogen can bind with basalt too, but Oxygen I think, binds more readily. Without photosynthesis and the creation of oxygen, not just life on earth but the continents would look very different and they'd probably be much less permanent.
So if all the volcanoes are under water, that limits the atmospheric absorption of oxygen and other gases to just what's disolved in the oceans which could be a lot of NH3, but relatively lower amounts of other gasses.
Another effect of all tectonic activity and volcanoes being under water is that volcanic gas like sulfates and tiny dust particles which can cool the planet after a large eruption, are unlikely to reach the atmosphere in any significant volume, so you're likely to avoid any volcanic cooling like you get on occasion on earth.
Finally, you might think that volcanoes under oceans would warm the oceans and they would locally, but not much overall. A significant percentage of Earth's volcanoes are under water, but because ocean water circulates, most of the deep oceans stay at a chilly 4 degrees C, as opposed to land which gets warmer as you dig into the ground. Convection circulates heat much faster than conduction.
Undersea volcanoes in your water world could be very helpful in the continuation and maintenance of extremophile life due to repleneshment of nutrients but not much in the way of temperature change or cloud formation.
Finally - a fun bit worth mentioning. NH3, which is a very common gas/ice in the solar system. It's in all the outer planets and comets and outer moons. The neat thing about NH3 is it's water soluble and it's an energy source to primitive life, so simply by having oceans, stinky but useful NH3 is fairly quickly, mostly removed from the atmosphere and dissolved in liquid oceans and if there's life, it can be consumed, some released as N2 or NO-family and some can be built into amino acids. Some nitrogen can bind with basaltic rock and magma from undersea volcanoes forming different types of rock, but I'm no geologist, so I'm not sure how much that would happen.
There's no one simple answer to this, but that's my best guess as a layman. I enjoy thinking about stuff like this.
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