First thing first, I wouldn't add it if it was clean and whole, as if the crab had just died and the birds had eaten all the juicy parts. Which begs the question, are there any soft, flexible parts attached (like legs)? If so, they need to come off as they are probably full of rotting flesh and muscle.
Soak it in some water and see how well it cleans up with some light scrubbing. Do NOT use any vinegar as it will probably eat more holes in the shell. We soaked some big, thick conch shells in some 50:50 water and vinegar and the shells starts to dissolve right in front of our eyes!