Make dip: Pulse sour cream, mayonnaise, blue cheese, Worcestershire sauce and vinegar in a food processor until mixture has blended into a chunky sauce. Season with salt and pepper. Cover and chill until ready to use. (Dip can be made up to 2 days ahead.)
Make chicken: Stir butter, hot wing sauce, sugar and vinegar in a pan over medium-low heat until butter has melted. Remove from heat. In a large ziplock bag, mix cayenne, 1 tsp. pepper, 2 tsp. salt and flour. Add half of chicken and toss until well coated.
In a large skillet, warm half of oil over medium-high heat. Remove chicken from bag, shaking off excess coating. Add to skillet and cook, turning on all sides, until chicken is crispy and no longer pink in the middle, about 6 minutes. Drain on paper towels. Wipe out skillet and repeat, tossing remaining chicken in coating and cooking in remaining oil.
Rewarm hot sauce mixture in a pan or microwave. Pour over chicken in a large bowl; toss well to coat. Thread 2 pieces of chicken onto 20 small skewers. Serve with dip and carrots and celery, if desired.