Pour enough oil into a skillet to cover wontons (about 1/4 inch deep). Heat oil to 350° F or on medium-high heat. Lay as many wonton wrappers as will fit into your skillet into the oil and fry until light golden brown, turning over to cook both sides (about 15-20 seconds per side). Adjust heat as necessary so wontons don't cook too quickly or take too long to cook. (Note: Cooking too quickly might burn wontons.) Drain fried wontons on paper towels. Set aside.
Crab Salad
In a medium mixing bowl, combine crab, celery, chives and grated lemon peel. In a small mixing bowl, stir together mayonnaise, lemon juice and pepper, then add to crab mixture and gently toss to combine.
Avocado Creme
Place avocado pulp, salt, lemon juice and cream in a small mixing bowl and smash and stir until well blended (small lumps are normal). Cover and refrigerate until ready to use.
Preheat oven to 400° F.
Top each wonton with crab salad and spread almost to the edges. Sprinkle each wonton with 1 tablespoon shredded cheese. Place wontons on a baking sheet and heat in the oven just long enough to melt the cheese (about 1-3 minutes).
To serve, arrange 3 wontons on each plate with a spoonful of Avocado Creme on the side. Garnish with chives if desired.