Preheat the broiler.
Cut the chicken wings in thirds, cutting between the bones. Discard the wing tips. Melt the butter and add the cayenne, hot sauce, and salt. Put the wings on a sheet pan and brush them with the melted butter. Broil them about 3 inches below the heat for 8 minutes. Turn the wings, brush them again with the butter, and broil for 4 more minutes or until cooked.
For the sauce, place the blue cheese, mayonnaise, sour cream, milk, Worcestershire, salt, and pepper in the bowl of a food processor fitted with a steel blade. Process until almost smooth.
Serve the chicken wings hot or at room temperature with the blue cheese dip and celery sticks.