Heat gas or charcoal grill. In small bowl, mix all dipping sauce ingredients. Refrigerate until serving time.
Cut each chicken wing at joints to make 3 pieces; discard tip. Sprinkle chicken wings with 1 teaspoon salt, the black pepper and red pepper.
Place wings on gas grill over low heat or on charcoal grill over indirect heat. Cover grill; cook 20 to 30 minutes, turning once, until golden brown on outside and no longer pink in center.
Place chicken wings in large bowl. In small bowl, mix pepper sauce and melted butter. Pour over wings; toss until well coated.
Serve chicken wings with blue cheese dipping sauce, celery and carrots.
The cayenne pepper will make the wings very hot. For medium wings, omit the cayenne. For mild wings, omit the cayenne and use a sweet barbecue sauce instead of the red pepper sauce.
For very crispy wings, grill until the chicken skin is slightly charred.