For the slaw, peel and slice the apple. Finely chop the apple, celery, green onion, and parsley. Toss these into a bowl along with the coleslaw mix and cheese; stir to combine. Whisk together oil, vinegar, sugar, salt, and black pepper; add to the slaw, stir to blend, and chill until serving time.
In a big zippered plastic bag, mix the wing sauce, melted butter, and ketchup; remove ½ cup and set aside for brushing on later. Add the chicken to the bag and toss to coat. Marinate at least 30 minutes.
To cook, set the chicken on a greased grate over indirect heat; discard the marinade remaining in the bag. Cook until the internal temperature reaches about 155°, turning to brown both sides. Move the chicken to direct heat, brush with set-aside marinade, and cook until the internal temp reaches 160°. Remove from the heat and cover with foil for 5 to 10 minutes.
Spread softened butter on the cut sides of the buns and toast on the grate. Set the chicken on the buns; drizzle with ranch dressing and load on the slaw.