In the container of a food processor, combine the celery, green onions, onion, and parsley. Pulse until finely chopped. Add the vinegar, ketchup, tomato puree, mustard and Worcestershire sauce.
Process until well blended, stopping to scrape down the sides a couple of times. With the food processor running, drizzle the oil in a steady stream, processing until blended. Stir in paprika. Transfer to a bowl, cover and refrigerate for 6 to 8 hours, or overnight. When ready to serve, stir the sauce, then pour over the shrimp and toss to coat. Serve on top of lettuce leaves.