I don't know what zombie lore you are watching but its stupid if zombies can't swim. Dead bodies often float anyway. I look at them like rabid animals and all animals can swim. Game play always beats "your favorite zombie lore". We could be heavy handed and make it so treading water eats stamina and you die if you can't reach the shore in time, which we might yet.
There simply cannot be a situation where there is a short action that leads to being fully safe in any situation, such as digging a 2 meter hole and jumping in it in the past.