Preheat oven to 450º.
Coat a large baking pan with cooking spray.
In a medium bowl, which together egg whites, 1/2 cup of flour, beer, baking powder and salt.
Place remaining 1/4 cup of flour in one bowl.
Place coconut and panko into another bowl.
Holding shrimp by their tails, dredge each shrimp in flour and shake off any excess.
Dip flour-coated shrimp into egg batter and allow excess to drip off.
Roll shrimp in coconut/panko mixture and turn to coat both sides (press coconut into shrimp to make it stick).
Transfer shrimp to prepared baking sheet and spray surface of shrimp with cooking spray.
Bake until coconut is golden brown and shrimp are bright pink and cooked through, about 10 to 12 minutes