Heat about 2-inches of oil in a heavy-bottomed pot or large Dutch oven over medium heat until a deep-fry thermometer registers 350 degrees F.
Meanwhile, put the eggs in one shallow dish. Whisk the flour, cornstarch, cayenne, 2 teaspoons salt and 1 teaspoon pepper together in a medium bowl. Transfer half the flour mixture to a third bowl and stir in the coconut.
Working in batches, dredge the shrimp in the flour mixture, shake off any excess, dip in the eggs, and then roll in the coconut mixture, pressing to coat thoroughly. Fry until golden, 2 to 3 minutes, adjusting the heat as needed to maintain the oil temperature. Transfer the shrimp to paper towels to drain. Serve with sweet chili or sweet and sour sauce on the side for dipping.
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