Set up a dredging station with three shallow dishes. Place the flour in the first shallow dish and season well with salt and freshly ground black pepper.
Whisk the eggs in the second shallow dish.
In the third shallow dish, combine the breadcrumbs, coconut, lime zest, salt and cayenne pepper.
Pre-heat the air fryer to 400F.
Dredge each shrimp first in the flour, then dip it in the egg mixture, and finally press it into the breadcrumb-coconut mixture to coat all sides.
Place the breaded shrimp on a plate and spray on all sides with vegetable oil.
Air-fry the shrimp in two batches, being sure not to over-crowd the basket.
Air-fry at 400F for 5 to 6 minutes, or until the shrimp is firm when you squeeze it gently. Repeat with the second batch of shrimp.
Lower the temperature of the air fryer to 340F. Place the first batch of shrimp into the basket with the second batch already in the basket and air fry for an additional 2 minutes.
Serve with sweet chili sauce, duck sauce or just eat them plain!