Choose 4 short metal skewers that fit fully inside a 6-quart air fryer with clearance from the element. Preheat to 390°F for 3 minutes.
Toss chicken, onion and zucchini with oil, lemon juice, oregano, salt, garlic powder and pepper. Thread onto the skewers, alternating ingredients and leaving small gaps.
Place 2 skewers in the basket without overlap. Air fry for 6 minutes, turn carefully and cook for 6 to 8 minutes more until the largest chicken pieces reach 165°F.
Transfer to a plate and repeat with the remaining skewers. Keep cooked skewers uncovered while waiting.
Rest the final batch for 3 minutes and serve one skewer per person, warning that the metal remains hot.