Laying hens need a certain amount of calcium for the egg shells. That calcium can come from a lot of different places. Layer feed has excess calcium. If Layer is all they eat, they probably don’t need any other source. Many plants contain calcium. Many bugs, especially hard-shelled bugs, can provide calcium. If you live in limestone country the rocks they eat for grit may provide a lot of calcium. Wild birds need some calcium for their egg shells and to build and maintain their skeleton. They have to get their calcium from nature, though their egg shells are often not as thick as chicken egg shells.
You can let your egg shells tell you if they are getting enough calcium. If they are hard and thick enough, they are getting enough calcium. If they are thin or soft, you need to supplement the calcium.
Shells are made of two different materials, chitin and calcium. Those soft flexible sort of clear parts of the crab are mostly chitin, a protein. They will eat those parts but they really don’t digest all that well where they will get a lot of benefit from them. Still, it is protein and they will get something.
The hard shell parts are mostly calcium. That’s what you are after. It doesn’t matter if that is oyster, clam, mussel, or crab shells, the harder it is the more calcium it has.
The reason oyster shells are so popular is because they are cheap. They dredge old dead oyster reefs to get the shell. Living oyster reefs are too valuable for the living oysters to be harvested for shell. There are massive dead oyster reefs all along the coast in many areas.
The only warning about using your crab and clam shells is that chickens can’t handle a lot of excess salt. Spices re fine but they can’t eat real salty food like sea gulls can. If you use a lot of salt when you cook those you might want to rinse them off with fresh water. Other than possible excess salt, you are good to go.