Carefully run a sharp paring knife through one side of the snow crab leg or claw to score the shell and allow easier access to the meat. Garde Manger serves its Caesar with crab crackers and forks. Guests are expected to work for it!
Pour the rim spice onto a small plate. Circle the rim of your glass with the lemon wedge, then roll the rim in the rim spice.
Pour the vodka, Caesar mix, horseradish, olive brine, hot sauce, and Worcestershire sauce into a cocktail shaker (or other mixing vessel). Fill the shaker with ice to just above the top of the liquid and stir with a bar spoon until the outside of the shaker is very cold to the touch.
Fill the rimmed glass three-quarters full with fresh cubed ice. Strain the contents of the shaker into the glass and top with additional ice if desired. Garnish with the snow crab leg (or claw) and the remaining lemon wedge.