Start with three shallow bowls. Combine tapioca flour, salt, pepper, and cayenne in one; set aside. Beat the egg in the second bowl; set aside. Place the shredded coconut in the third bowl; set aside.
Dip each shrimp into the flour mixture, then the egg, and then press into the shredded coconut.
Add enough oil to cover the bottom of a large sauté pan and heat over medium-high heat. Fry the shrimp in batches until golden brown, about 3-4 minutes per batch.