Preheat oil in a deep fryer, or deep-saucepan, to a temperature of 375 degrees. Blot hot dogs dry with a paper towel. Place several tablespoons of corn starch into a shallow pan and roll hot dogs in corn starch until they are well-coated. (Coating the hot dogs in cornstarch will help the batter stick to the hot dogs when they are deep-fried.) Insert wooden skewers (or chopsticks) into hot dogs deep enough to make a “handle,” trimming skewer as needed; set aside. In a medium bowl, mix the corn muffin mix, flour, egg, milk, dry mustard, paprika and cayenne, blending well. Pour batter into a tall iced tea or ice cream soda glass, filling about two-thirds full. Holding the hot dog by its stick handle, dip the hot dog into the batter, one at a time, allowing the excess batter to run off. Place hot dogs, no more than two or three at a time, into the hot oil, twirling them gently with kitchen tongs so they form a round shape. (Twirling the corn dogs helps to keep them from frying flat.) Deep-fry until a deep golden brown, about 3 to 4 minutes. Drain on brown paper or some paper towels. Makes 8 corn dogs.