In a small bowl mix together cayenne, black pepper, salt, and cornstarch; set aside.
Preheat oven to 200 degrees. Line baking sheet with paper towels. In a heavy saucepan that is at least 5 inches deep, heat 2 1/2 inches of oil over medium heat until it registers 360°F on thermometer. Dry chicken with paper towels and place pieces in large mixing bowl.
Sprinkle spice mixture over wings and toss until evenly coated. Fry chicken wings in batches for 10-15 minutes until golden brown.
Using tongs or a slotted spoon, remove wings to teh baking sheet lined with paper towels to drain. Keep first batch of chicken warm in oven while frying remaining wings.
In a small saucepan, over low heat, combine butter, hot sauces, brown sugar, and vinegar and stir until butter is melted. Remove from heat.
To make the Creamy Blue Cheese Dressing and Vegetables: in a small bowl, mash blue cheese and buttermilk with fork until mixture resembles cottage cheese with small curds. Stir in sour cream, mayonnaise and white wine vinegar; set aside.
To Serve: Pour sauce mixture into large bowl, add chicken wings, and toss until wings are coated.
Serve immediately with the carrot and celery sticks and blue cheese dressing on side.