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.