Preheat oven to 425°. Peel shrimp, leaving tails on; devein, if desired.
Place a wire rack coated with cooking spray in a 15- x 10-inch jelly-roll pan.
Whisk egg whites just until foamy.
Stir together cornstarch and jerk seasoning in a shallow dish. Stir together coconut, Japanese breadcrumbs, and paprika in another shallow dish.
Dredge shrimp, 1 at a time, in cornstarch mixture; dip in egg whites, and dredge in coconut mixture, pressing gently with fingers. Lightly coat shrimp on each side with cooking spray; arrange shrimp on wire rack.
Bake at 425° for 10 to 12 minutes or just until shrimp turn pink, turning once after 8 minutes.