Whisk the olive oil, lemon juice, lemon zest, honey, balsamic vinegar, garlic, oregano, salt, and pepper in a large bowl.
Add the chicken cubes and toss to coat. Cover and refrigerate for at least 30 minutes and up to 8 hours.
Soak wooden skewers in water for 20 to 30 minutes and trim to fit your air fryer basket.
Thread 4 to 5 chicken pieces onto each skewer, alternating with vegetables if using. Leave small gaps between pieces.
Preheat the air fryer to 400°F for 3 minutes. Lightly spray the basket with oil.
Arrange the kabobs in a single layer. Air fry for 5 to 6 minutes, flip, and cook 5 to 6 minutes more, until the chicken reaches 165°F. Work in batches if needed.
Rest for 3 minutes, garnish with parsley, and serve with lemon wedges.