The two alternatives I like the best are...
The Zelda alternative:
When you run out of stamina, you "drown" and end up on the shore where you entered the water,
losing a certain amount of hp; possibly all shp, knocking you out.
The Other alternative:
When you drown, you're swept away by the currents (yes, even in a lake) and end up on a shore
anywhere in the world, but preferably somewhere connected to where you drowned.