Clean and butterfly the shrimp, leaving the tails on. Pat dry with paper towels.
Set up a three-bowl station for battering the shrimp. In the first bowl, whisk together the flour, salt, and black pepper. In the second bowl, whisk together the egg and the rum. In the third bowl, whisk together the coconut flakes and the panko.
Dip the shrimp in the flour mixture and then the egg mixture. Press the coated shrimp into the panko coconut mixture, coating thoroughly. Spread out onto a baking sheet and chill in the freezer for around 30 minutes.
Preheat the air fryer to 375 degrees F. Spray with coconut oil.
Spread out the battered shrimp in a single layer in the air fryer basket. Air fry for 8 minutes, shaking halfway through.
Meanwhile, whisk together the dipping sauce ingredients. Add the water if the mixture seems too thick a little at a time until the consistency of loose honey.
Serve shrimp alongside dipping sauce as an appetizer or with a vegetable or rice if a main meal.