If by Shore crab you mean the green fast running ones (Carcinus maenas): yes, they're excellent but more of a snack than a meal. Very tasty but little meat. The French eat them but generally don't bother to bring them to market, except if they'" BBBig'unes.
The bigger purple hairy swimming crab (Portunus puber, sorry, don't know the English name) called étrille in French is considered an even greater delicacy. These are often sold alive in France. But apart from a snack, both can be turned into soup.
Recipe: water, veggies to your choice, salt pepper. Boil. Add crabs. Boil 30 mins. Crush or put into the blender. Sieve. Press the carapaces in the sieve to extract all the perfumes. Enjoy.
If you find the hairy whitish/blueish woolhand crabs (in estuaries or Freshwater): sell them to your chinese shop and buy lobster with the money you got from them