Peel and devein the shrimp, leaving the tails on. Place them on a sheet pan with the olive oil, salt, and pepper and spread them in 1 layer. Roast for 8 to10 minutes, just until pink and firm and cooked through. Set aside to cool.
For the sauce, combine the chili sauce, ketchup, horseradish, lemon juice, Worcestershire sauce, and hot sauce. Serve as a dip with the shrimp.