I would say that it could be any of the above. Corsairs tend to be young and foolish if they come from Craftworlds, so it would be easy for them to be so consumed in their arrogance that they leave their spirit stone or discard of it later on. In that case I think death would be a soul straight to Slaanesh type of thing.
If Commorrite then he might have been lucky enough to have secured a deal with a Haemonculus, but being a corsair makes me think they'd be spending most of their time in realspace.This then leads me to ask why are they spending most of their life in realspace? Have they been exiled from Commorragh? If so then it would be pretty hard to get brought back by your coven.
Being a prince he may very well be older and wiser than other corsairs, however. Even if from Craftworld origins he could have gone to Commorragh to strike a deal with Haemonculi.
So, I would say any! Do you have any written background for you Corsair Prince?