I think the biggest "zap" concern would be if you used regular headphones for a non-waterproof mp3 player. The mp3 player alone (without headphones or with proper waterproof ones) would be far more likely to short out internally, without any electricity passing through you.
Personally, I think the best solution to all of this would be to use a set of wireless waterproof headphones. It's easy to seal your phone up in a properly waterproof case, or properly wrap an mp3 player without any holes for leakage. Then you could just tuck it next to your hip under your swimsuit or something, or even lock it to the diving block and leave it on shore.
But, you'd have to find an mp3 player that will work with wireless/bluetooth headphones, or use your phone.
Edit: Found
this link which reviews some wireless waterproof headphones