Barbados cherry is one of the toughest things I've ever grown, if not the toughest. It won't be phased whenever you prune it.
That said, I'd only prune of the lowest limbs, because as the tree grows, its branches rise up and droop back down in a cascading form. The lower branches are the easiest to harvest from thi reason as they are on the outside of the bush, and the leaves have hairs which causes skin irritation.