In a shallow bowl, combine flour, garlic powder, paprika, salt, and black pepper. In another bowl, beat the eggs. In a third bowl, place the shredded coconut and panko breadcrumbs together.
Dip each shrimp first into the flour mixture, shaking off any excess. Then, dip it into the beaten eggs, allowing any excess to drip off. Finally, coat the shrimp in the coconut and panko mixture, pressing gently to adhere.
In a large skillet, heat about 1/2 inch of vegetable oil over medium-high heat until hot. Carefully add the shrimp in batches, making sure not to overcrowd the pan.
Fry the shrimp for 2-3 minutes on each side, or until golden brown and crispy. Remove the shrimp from the skillet and place them on a paper towel-lined plate to drain excess oil.
Serve the crispy coconut shrimp warm with lime wedges on the side.