In a bowl, mix together the shrimp, crabmeat, mayonnaise, chopped parsley, chopped radishes, chopped celery, shallots, lemon juice, cayenne, 1/2 teaspoon salt and a few grinds of pepper.
Halve and seed the avocados. Use a spoon to scoop out most of the flesh, leaving 1/4 inch behind. Chop the avocado flesh and gently mix it into the seafood salad. Add salt and pepper to taste. Spoon the seafood salad into the avocado halves.
Toss the arugula with the sliced celery, sliced radishes, parsley leaves, olive oil and a pinch of salt. Divide among 8 plates; nestle the avocado halves on top. Serve with lemon wedges on the side.