Serebii has the Egg groups posted up. Clawitzer is in Water 1 and Water 3, meaning it's alongside Clampearl/Huntail/Gorebyss, Omanyte/Omastar, Tirtuoga/Carracosta, and Shellder/Cloyster. There's a good chance it can learn Shell Smash, but until someone proves it, I wouldn't get my hopes up.