Fill a large bowl with the ice and cold water; set aside.
Bring the water, halved lemon and bay leaves to a boil in a large pot. Add the shrimp and cook until pink and just opaque, 2 to 3 minutes.
Lift the shrimp into the ice bath with a slotted spoon and chill 5 minutes. Drain, pat dry, and discard the poaching liquid.
Stir together the ketchup, horseradish, 1 tbsp lemon juice, Worcestershire, hot sauce and salt.
Serve the chilled shrimp with the sauce and lemon wedges, or refrigerate both for up to 24 hours.