Heat 3 inches of oil in a large deep skillet or heavy pot to 325 degrees F.
In a small bowl, mix the cornstarch, egg whites, salt, and pepper until foamy. Spread the coconut out in a pie dish. Dredge the shrimp with the cornstarch/egg white mixture and shake off any excess. Press the shrimp into the coconut flakes; turn shrimp over and press into coconut again to coat both sides.
Deep-fry the shrimp in batches until the coconut is golden brown, about 2 to 3 minutes. Using tongs or a slotted spoon, remove the shrimp to paper towels to drain. Arrange the shrimp on a platter, serve immediately with red curry sauce and garnish with green onion and mint.
Red Curry Sauce:
Place a small pot over medium heat and coat with the oil. Stir the red curry paste into the pan and fry until aromatic. Slowly pour in the coconut milk and continue to stir to incorporate. Add the lime juice (and 1 of the squeezed out halves for added flavor) and cook for 5 to 10 minutes to thicken. Pour the sauce into a nice serving bowl and serve with the coconut shrimp.