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