Refrigerate chicken in pickle brine 30 minutes, included in prep time. Drain, pat dry, and unfold thighs evenly.
Preheat a 6-quart air fryer to 390°F for 3 minutes. Beat egg with water; separately mix flour, cornmeal, salt, paprika, and pepper.
Dip chicken in egg; press into cornmeal mixture and dab with oil until no dry patches remain. Arrange both thighs without touching.
Air fry 8 minutes; turn and cook 8 to 10 minutes more until crisp and at least 165°F. Rest on rack 3 minutes.
Spread buns with mayonnaise; add dry lettuce, chicken, and pickles. Close; serve one sandwich per person.