This was addressed in Miyazaki, Conjugation and the prime decomposition of knots in closed, oriented 3-manifolds, using the definition of connected sum suggested by Ryan Budney in the comments.
The main results are that a prime decomposition of K exists iff a meridian of K is not null-homotopic in the complement of K, and if a prime decomposition of K does not contain a particular knot R in S1×S2 then it is the unique decomposition of K, whereas knots with this summand R can admit several prime decompositions.
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