Classic Shrimp Cocktail Classic Shrimp Cocktail also known as Prawn Cocktail in some areas has been around for many, many years. Oysters were the original 'cocktail' shellfish, usually served as an appetizer in tiny cups and served with a spicy, ketchup sauce containing horseradish and Tabasco sauce. 'Cocktails' became extremely popular during the 1920's, the decade