Stir together the ketchup, horseradish, lemon juice, Worcestershire and hot sauce. Cover and refrigerate.
Fill a large bowl with ice and water.
Bring a large pot of water to a boil with the salt. Squeeze in the lemon half and drop it in.
Add the shrimp and cook for 2–3 minutes, just until pink and opaque.
Drain and move the shrimp straight to the ice bath. Chill for 5 minutes, then drain and pat dry.
Refrigerate until ready to serve, at least 15 minutes. Serve with the cocktail sauce and lemon wedges.
