1. In processor, finely chop peppers. In saucepan, cook peppers, ketchup, onion, salt, horseradish, vinegar, Worcestershire, pepper sauce over medium-high, stirring, 5 minutes. Remove to bowl; let cool. Cover and refrigerate.Shrimp:
2. In large saucepan, bring 3 quarts water, celery, lemon to boiling. Add shrimp; boil 1 minute, until shrimp are pink and cooked. Drain; rinse under cold water. Peel, leaving tails on; devein. (Sauce, shrimp can be fixed a day ahead.)
3. Halve, pit and peel avocados. Place crushed ice in bottom of 6 large glass bowls. Place avocado half on top. Fill avocado center with cocktail sauce. Arrange shrimp hanging over edge of glass. Pass remaining cocktail sauce.