When attempting to wield claws while also wielding a Crab claw in your glove slot, you will get a message saying "You need to remove your claw first." You can still wield claws while wielding a Pirate's hook or the Crabclaw hook.
Unlike other weapons, claws used to have the option to "wear" instead of "wield". This was unique, as only equippable non-weapon items have this option.
Claws used to exist in pairs, as a single item. They were separated into individual main-hand and off-hand claws with the Evolution of Combat update. Before this, they were among the fastest two-handed weapons in the game.