Prepare the shrimp: Rinse the shrimp under cold water and pat dry with paper towels. Set aside.
Set up the breading station: In a shallow dish, whisk together the flour, salt, black pepper, garlic powder, onion powder, paprika, and cayenne pepper. In another shallow dish, beat the eggs with water until well combined. In a third shallow dish, mix together the shredded coconut and panko breadcrumbs.
Bread the shrimp: Hold a shrimp by the tail, then dredge it in the flour mixture, shaking off any excess. Next, dip the shrimp into the egg mixture, allowing any excess to drip off. Finally, press the shrimp into the coconut-panko mixture, ensuring it is well coated on both sides. Place the breaded shrimp on a plate or tray and repeat with the remaining shrimp.
Heat the oil: In a large, deep skillet, heat the vegetable oil over medium-high heat until it reaches 350°F (use a thermometer to monitor the temperature). If you don't have a thermometer, test the oil by dropping a small pinch of the coconut-panko mixture into the oil - it should sizzle upon contact.
Fry the shrimp: Working in batches, carefully place the breaded shrimp into the hot oil, making sure not to overcrowd the skillet. Fry for 2-3 minutes per side or until the shrimp are golden brown and cooked through. Use a slotted spoon to transfer the cooked shrimp to a paper towel-lined plate to drain any excess oil.
Serve: Serve with sweet chili sauce or mango chutney for dipping, if desired.