I think you’re right that they regurgitate food for their young like most birds. A unique puke related vulture fact is that they projectile vomit at predators as a deterrent and means of dropping weight to flee after they’ve been gorging on a carcass.
If swimming wasn’t the first event, I’d like my odds. I don’t like the idea of swimming at the same time as the shark, even if eating your opponent is grounds for disqualification.