Heat the oven to 400°F. Line a large rimmed baking sheet with parchment and set a wire rack on top if you have one. Pat the shrimp very dry with paper towels.
Set up three shallow bowls: flour in the first, beaten eggs in the second, and the shredded coconut, panko, garlic powder and salt stirred together in the third.
Holding each shrimp by the tail, coat it in flour and shake off the excess, dip it in egg, then press it into the coconut mixture so both sides are covered.
Arrange the shrimp in a single layer on the rack or parchment, spacing them apart, and brush the tops with the melted coconut oil.
Bake 12 to 14 minutes, flipping once halfway through, until the coating is golden and the shrimp are opaque and curled.
While they bake, stir the mayonnaise, sweet chili sauce and lime juice together. Serve the shrimp warm with the dip and lime wedges.
