Line a rimmed baking sheet with foil. Add shrimp to a bowl, drizzle with olive oil, sprinkle with salt and pepper. Mix until coated. Turn out onto sheet pan and spread into an even layer.
Roast for 8 to 10 minutes, or until the shrimp turn pink and firm.
To make the cocktail sauce, combine ketchup, chili sauce, horseradish, lemon juice, Worcestershire, and hot sauce. Mix until well combined.
Pour sauce into a dish and serve with shrimp and extra lemon for squeezing.