If the wings are whole and not yet separated, use a chef's knife or kitchen shears to cut through the first joint of the wing and remove the wing tip. Then chicken dry with paper towels salt it.
Place on a wire rack in a 15x10x1-in. baking pan. Refrigerate at least 1 hour or overnight.
In an electric skillet or deep-fat fryer, heat oil to 375°. Fry wings in batches until skin is crisp and meat is tender, 8-10 minutes. Drain on paper towels.
For Buffalo wing sauce, bring hot sauce just to a boil in a small saucepan. Remove from heat; whisk in butter one piece at a time. Stir in molasses and cayenne pepper.
Toss with the remaining buffalo sauce. Drizzle the reserved hot sauce over the wings and toss to coat.
Serve immediately. Transfer the wings to a serving tray and serve while still piping hot with the blue cheese dressing and celery sticks.