I’d be wary of a waterproof type sheet as surely that could overheat the back of the little ones head on warmer days.
Hardly, the child will be lying on it, not wrapped in it, and I can’t see any difference between such a blanket used on a normal bed, and in a hammock, which has air circulation all round. In any case, it’s supposed to prevent leakage from the bottom half, not the top*, the blanket doesn’t have to be under the child’s head at all, does it.
*Yes, I know that children can ‘leak’ from the top end, but that sort of ‘leakage’ is less likely to pour through a normal sheet used to line a hammock, and I doubt any child could produce enough snot for it to pour through onto the unfortunate people underneath! 😀