Place enough oil in a deep, heavy skillet to reach about 1 inch up the sides. Alternately, you can use a deep fryer.
Heat oil to 375 degrees (a cube of bread should brown in 1 minute if oil is the correct temperature).
Remove shells and vein from shrimp, but leave tail on as it makes it convenient for dipping.
In a small bowl, mix the flour, baking powder, salt, cayenne and egg. Add just enough of the ice water to make a thick batter that will cling to the shrimp.
Place shredded coconut on a flat plate, dip shrimp in batter, then coat with coconut.
Place shrimp in hot oil and deep fry for about 3 to 5 minutes on each side, or until golden brown.
Remove to parchment-covered plate to keep warm if frying another batch