On the Bodoodle I had, I put moleskin on the underside of the fins to muffle the twang and used the nail hardener on topside. Mine had a carriage return spring that I also had to put a bit of soft foam rubber inside to deaden the twang from the spring.

I don' t know if yours has a spring or not (haven' t kept up with Bodoodle for a few years now so I don' t have a clue what the Zapper is), but if it does, try the foam rubber in the spring. Just enough to make contact with the coils, but not so much as to interfere with the workings.