For remoulade, in a small bowl combine vinegar, catsup, horseradish mustard, paprika, and ground red pepper. Slowly add oil while beating with a whisk or fork; beat until combined. Stir in celery and green onion.
Place cooked shrimp in a plastic bag set into a bowl. Pour remoulade over the shrimp. Seal bag. Turn bag to coat shrimp. Marinate in the refrigerator for 1 to 2 hours, turning occasionally.
To serve, drain shrimp, reserving marinade. Divide greens among 4 dinner plates. Halve, peel, and seed avocados. Slice avocados and arrange on torn greens. Arrange shrimp over avocados. If desired, garnish with beets, hard-cooked egg, and lemon peel. Stir and pass reserved marinade. Makes 4 main-dish servings.