Prep the sauce: In a small bowl, mix sugar-free ketchup, horseradish, lemon juice, Worcestershire, hot sauce (if using), and a pinch of salt. Taste and adjust horseradish or lemon to your liking. Chill while you cook the shrimp.
Make the creamy layer (optional): In another bowl, combine cream cheese (or mashed avocado), mayo, lemon zest, salt, and pepper.
Stir until smooth. Set aside.
Season the shrimp: Pat the shrimp dry. Toss with olive oil, salt, pepper, paprika, and garlic powder.
Cook the shrimp: Heat a skillet over medium-high.
Add shrimp in a single layer and cook 1–2 minutes per side until opaque and just pink. Do not overcook. Transfer to a plate to cool slightly.
Slice the cucumber: Cut into 1/4-inch rounds.
If the centers are very seedy, lightly pat with a paper towel so toppings grip better.
Assemble the bites: Spread a thin layer of the creamy mixture on each cucumber round (about 1/2 teaspoon). Add a small dollop of cocktail sauce on top.
Top with shrimp: Place one shrimp on each round. If you left tails on, angle the tail upward for a pretty presentation.
Garnish and finish: Sprinkle chopped dill or chives over the top.
Add a squeeze of lemon just before serving, or serve with lemon wedges on the side.
Serve: Arrange on a chilled platter. These are best slightly cool but not icy cold, so the flavors pop.