I peel the shrimp and remove the tail. I don't want the hard sharp edges even possibly injuring them inside. It's not worth the risk. But i don't know if I'm being an overprotective mother.
Oscar is in my opinion is an easy eater. Had a few when i first start out. They will eat float and sinking pellets, other fishes, and raw shrimp that was mean for my arowanas. They will stuff their mouth full even if they can swallow.
Uncooked would be the first choice but if you cant find it then cooked is fine. For safety reasons I would take both the tail and shell off. It would be terrible if your oscar died because it choked to death on a tail or the shell.