Juice and zest one lemon. In a large bowl, combine lemon juice and zest, yogurt, garlic, olive oil, dried oregano, dried thyme, salt, and pepper.
Add chicken pieces to marinade and toss to coat. Cover and refrigerate 2 hours to overnight.
To make feta sauce, combine all ingredients in a food processor and blend until smooth.
Slice remaining lemon into small wedges (1 large lemon should yield about 16 small ½ wedges). Thread chicken and lemon wedges onto skewers, being sure the skewers will fit in your air fryer.
Set air fryer to 350 and arrange skewers in a single layer. Cook 8 minutes. Flip, and cook another 8 minutes.
Serve skewers with dipping sauce, squeezing cooked lemon over them as desired.