In shallow dish, combine flour, salt and cayenne pepper; set aside. Place coconut in another shallow dish; set aside. In a small bowl, beat egg whites until frothy.
Dredge shrimp in flour mixture, then eggs. Roll in coconut. Place on a large baking sheet that has been generously sprayed with olive oil cooking spray.
Spray tops of shrimp with cooking spray. Cover with aluminum foil. Bake in a preheated 500°F oven for 5 minutes. Remove foil and continue baking until shrimp are cooked through and coconut is golden brown (about 5-6 minutes longer).