Preheat oven to 425ยบ F. Line a rimmed baking sheet with foil, and place a cooling rack on top of the foil. Spray the cooling rack with nonstick cooking spray.
In a small bowl, combine the coconut flour, cayenne, sugar, and salt. Set aside half of the mixture in a separate bowl, because the mixture can become clumpy halfway through the breading process.
In another small bowl, whisk together the egg whites and the juice from half of the lime.
Set up a shallow dish with the coconut flakes.
Dip each shrimp into the coconut flour mixture, then the egg mixture, and then the coconut flakes. Place each shrimp flat on the baking sheet.
Bake until the coconut flakes are lightly golden, 10-15 minutes. Squeeze the juice of the remaining half of the lime over the shrimp and serve.