Season chicken with pepper. Put flour in one shallow dish, beat eggs in another and put crushed pretzels in a third.
Coat cutlets in flour, egg and pretzel crumbs, pressing gently so the coating sticks. Brush both sides with the measured oil.
Preheat air fryer to 375°F. Cook two cutlets in one layer for 12 to 16 minutes, turning halfway, until the centers reach 165°F; repeat with the other two. Keep the first batch on a rack in a 200°F oven while the second cooks.
Warm hot sauce and butter in a small saucepan just until melted. Stir yogurt, mayonnaise, dill, garlic powder, celery seed and lemon juice together in a separate bowl.
Toast the cut bun faces under the broiler for about 1 minute. Brush the cooked cutlets lightly with Buffalo butter, using the sauce evenly across all four.
Spread ranch on the buns, add iceberg, one hot cutlet and drained pickle chips to each, then close and serve immediately.