The wording doesn't specify and it could go either way.
Looking at one ability that definitely lets the ability-owner choose is the Yin's devotion ability, and that makes it a point to explicitly point out that the Yin player chooses. "Produce 1 hit and assign it to one of your opponent's ships." If it had just said "produce one hit", I think most would assume that the target gets to choose. The Exotrireme ability is like if they left out the part about getting to assign it, but yet the wording is still ambiguous.
Official call on this? (personally I think the N'orr getting to pick would be a little crazy)
Edited by GrooveChamp