Bring a large pot of salted water to boil. Add shrimp and cook for 2-3 minutes until pink and opaque. Drain and immediately transfer to an ice bath to stop cooking.
In a medium bowl, whisk together ketchup, horseradish, lemon juice, and Worcestershire sauce until smooth. Refrigerate until ready to use.
Spoon about 2 tablespoons of cocktail sauce into the bottom of each cup.
Hook 2 shrimp over the rim of each cup, letting them hang attractively.
Garnish each cup with a small sprig of fresh dill or parsley and a tiny lemon wedge.
Keep refrigerated until serving time. These can be made up to 4 hours ahead!