I think there's a deleted scene where he ties himself to the periscope with his whip, and waits it out there. Still, that'd be a long time to wait, judging by the distance they traveled via the map.
In fact, I found a page that discusses the sequence, complete with a script excerpt and a picture of the scene from the comic:
So according to the script, how does the sub scene unfold? Well, the boat starts going under, but stops when just the top of its periscope is breaking the waves. Indy clings to the scope and gets dragged along. He then uses his whip to actually tie himself to the periscope, where he dangles for the entire trip, watching as shark fins circle him. Finally…
Full article, with script excerpt and photos here.