Id I were making one, I would kleave the lower jaw loose (maybe using a leather hinge to affix it to the head proper) and then rig the lower jaw with a string that I would then run through a hole in the head piece and back between the ears to my hand. Then, I could pull the jaw shut for a "snap" on command. I think that would be more effective than spring-loading it, because I wouldn't have to move the whole head in order to make the jaw "bite."

My neighbor made a similar critter for a hoodening ritual we did for our apple orchards a few years ago, and I think that's how he rigged it but can't recall for sure.