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