Welllll
Assuming you mod sharks to have children, and remember not to give them [LAYS_EGGS] because that won't work underweater
The first consideration is that dwarves will only train
Wild animals in cages; and no creature which has ever been Wild can ever be Tame. So in order to train your pups up to Tame, they're going to need to be in a training zone. Since dwarves cancel jobs in 4/7 water, and sharks should air drown in 4/7 water or less, this should be impossible with living Animal Trainers unless you mod in some sort of "give a dwarf the [AMPHIBIOUS] tag" reaction.
However.
Sometimes, a dwarf who dies with points in Animal Training, and Animal Training enabled,
will continue taking Train Animal tasks after death (though you can't assign them explicitly - you need to set your animals to "any trainer"). A ghostly animal trainer should have no problem training an animal underwater.
The exact circumstances needed to trigger this bug are not yet clear, but, if you are
dead set on tame shark dorfy awesomeness, you could try training up a gaggle of peasants to Novice animal trainers, atom smashing them, and not memorializing them.
You know, for science.
Edit: clarified my egglaying comment