- Combine the salt, pepper, and cayenne in a large container with a tightfitting lid or a large resealable plastic bag. Add the chicken and toss with your hands until evenly coated. Close the container and refrigerate at least 30 minutes and up to 2 hours.
- Meanwhile, place the maple syrup, Dijon mustard, whole-grain mustard, vinegar, and soy sauce in a small, nonreactive bowl and whisk to combine; set aside.
- Heat an outdoor grill to medium high (about 375°F to 425°F). When the grill is ready, use tongs to rub the grate with several layers of paper towels dipped in vegetable oil. Place the wings on the grate in a single layer so they are not touching (if needed, cook them in batches). Cover the grill and cook, flipping the wings occasionally with tongs, until the skin is opaque and no longer raw-looking, about 10 minutes. Brush all over with the reserved maple-mustard sauce and continue to cook, flipping and basting occasionally, until the wings are golden brown, no longer pink at the bone, and the skin is crisp, about 10 to 15 minutes more.