Preheat oven to 425 degrees.
Peel and devein shrimp, leaving tails on.
Salt shrimp to taste.
Place a wire rack coated with cooking spray in a jelly-roll pan.
Whisk egg whites in a bowl until foamy.
Place cornstarch into a shallow dish.
Stir together coconut, breadcrumbs, and paprika into another shallow dish.
Dredge each shrimp in cornstarch, shaking off excess.
Dip in egg whites.
Dredge in coconut mixture, pressing gently with fingers.
Lightly coat shrimp with cooking spray.
Place shrimp on wire rack.
Bake at 425 degrees for 16 minutes or just until shrimp turn pink, turning after 8 minutes.