Animating hair over sprite animation

So I have a character sprite sheet animated such that they can walk with different moods (happy/angry/etc) as well as sit with those moods. I'm now trying to add random hair variation to each one, but I don't want to have hundreds of animations for each type of hair to follow the character's head (as it moves slightly up and down each frame). Is there a way to add the hair on top of the head and have Unity animate it?