In deep fat fryer or heavy saucepan, heat 3 inches oil to 375 degrees F. In medium bowl, stir cornbread mixes, club soda and egg. Spoon mixture into tall narrow jar or glass. Insert sticks into hot dogs, leaving about 4 inches to hold. Roll hot dogs in flour; dip hot dogs into cornbread mixture, rolling to cover completely. Smooth batter with knife, if necessary.
Fry 2 to 3 corn dogs at a time in hot oil about 2 to 3 minutes or until golden brown. Drain on paper towels. Serve corn dogs with mustard.