when you're moving in a direction the snake wants to go too (so you're not pulling it) you are not loosing stamina and in fact regaining it.
so the trick is to lure the snake as close to the shore as possible and only pull it out for the last few meters.
(i usually use 2 or 3 stamina foods for this though)

on the other hand you only need scales to get yourself a shield. i don't think there are any more uses for it. after that you just kill it in a water and get meat (wich i think floats)