In shallow dish, combine bread crumbs, coconut and ¼ cup corn starch. In second shallow dish, combine remaining corn starch, salt and cayenne pepper. In third shallow dish, beat egg whites until frothy.
Dust shrimp with corn starch, dip in egg and coat with bread crumbs. Set aside.
In large skillet with high sides, fill halfway with oil. Heat over medium-high heat until oil reaches 375°F or small amount of bread crumbs sizzles when placed in the hot oil.
Working in batches, carefully place shrimp in hot oil being sure not to over crowd. Fry until golden brown and shrimp are opaque in the center (about 3-4 minutes). Remove to clean paper towels to drain.