Pat dry and season: Blot the chicken dry with paper towels.
Season all sides with salt and pepper. Drizzle with oil and rub to coat evenly.
Make the sauce: In a small saucepan, whisk together sugar-free ketchup, apple cider vinegar, Worcestershire sauce, mustard, smoked paprika, garlic powder, onion powder, liquid smoke (if using), and your sweetener. Bring to a simmer over medium-low heat for 5 to 7 minutes, stirring often, until slightly thickened.
Taste and adjust sweetness, salt, and heat.
Preheat your cooking method: Grill: Heat to medium (about 375–400°F). Oil the grates.
Oven: Preheat to 400°F. Line a sheet pan with foil and set a wire rack on top, if you have one.
Air fryer: Preheat to 375°F for 3 minutes.
Start cooking without sauce: Cook the chicken skin-side down first to render fat and crisp the skin. Grill: 12–15 minutes, turning once or twice.
Oven: 20 minutes on the rack.
Air fryer: 14 minutes, flipping halfway.
Baste and finish: Brush on a generous layer of sauce and continue cooking until the chicken reaches an internal temperature of 165°F for thighs/drumsticks (measured at the thickest part, not touching bone).
Add another layer of sauce in the last few minutes to set a glossy finish. Grill: 8–12 more minutes, turning and basting as needed.
Oven: 10–15 more minutes, brushing twice.
Air fryer: 6–8 more minutes after first baste.
Rest and serve: Let the chicken rest for 5 minutes. Brush with a final spoonful of sauce. Serve with cauliflower “potato” salad, grilled zucchini, or a crisp slaw.