At least two hours before you plan to serve the shrimp cocktail, poach the shrimp. Begin by preparing a poaching liquid. Fill a large pot—like a stock pot—with water. Squeeze the juice of the lemon halves into the water, and then add the lemon halves to the water as well. Bring the pot of water to a boil, and then turn the heat down so that the water is at a low simmer. Add the shrimp, cover the pot, and let them poach for about four minutes. Right at the four minute mark, check the shrimp for done-ness, and if they're bright pink and firm, immediately turn the heat off. Cover the pot again, and let it stand for about two minutes. Drain the shrimp. Once they've cooled enough for you to comfortably handle them, shell them and devein them. Chill for two hours before serving.
In a small bowl mix together everything except the shrimp and lemon until cocktail sauce is smooth. Serve with steamed shrimp over ice with lemon wedges.
