Beat egg, mustard and water in a shallow bowl. Mix flour, cornstarch, salt, paprika, onion powder and pepper in a second bowl.
Pat drumsticks dry, dip in egg mixture and press into the flour mixture. Set on a plate for 10 minutes so the coating hydrates.
Preheat an 8-quart air fryer to 380°F for 3 minutes. Dab the drumsticks with oil until no powdery flour patches remain and arrange in one layer with gaps.
Air fry for 12 minutes, turn gently and cook for 13 to 17 minutes more until golden and the thickest meat reaches 175 to 185°F, always at least 165°F. Dab any newly exposed dry flour with the remaining measured oil during the turn.
Rest on a rack for 5 minutes and serve one drumstick per person.