What I was getting at is that there isn't a strong connection between the people that ran the ships and the people who bought slaves once they were off-loaded.The point is, though, that many nursery rhymes have very long histories, and it doesn't matter whether or not those keeping them alive between the time they were first composed and today (or whenever they dropped from general view) were ever participants in the events on which the rhymes were based.
After all, the children singing/reciting them down the ages weren't, so why should those sailors have been?
But "pick" also can mean "cull", and the rhyme may refer to the shipboard process of finding and removing dead slaves from the hold and tossing their bodies overboard in transit.
Or, it can be a silly reference to Brazil nut harvesting. It is kind of hard to tell 200 years later, but the fact that this was big in England would appear to make it less likely to be directly from market patter within the colonies. (None of which is a judgement about the merits, just the etymology.)