Prepare the Dipping Sauce: In a bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, Worcestershire sauce, hot sauce, and horseradish (if using). Season with salt and pepper to taste. Cover and refrigerate for at least 30 minutes to let the flavors develop.
Crack the Claws: Gently crack each crab claw using a seafood cracker or the back of a spoon. Try to avoid crushing the shell completely to keep the meat intact. Remove any sharp shell edges.
Serve Chilled: Arrange the cracked claws over crushed ice on a platter. Garnish with lemon wedges and serve with the chilled mustard dipping sauce on the side.
Enjoy Immediately: Stone crab claws are best served cold and fresh. Dip into the sauce, and enjoy!