Preheat oil in a heavy bottomed pan to 375°. Mix together the flour and corn muffin mix. Next mix in egg, milk, mustard, paprika, and cayenne just until combined. Lightly coat the Li'l Smokies with flour.
Using a toothpick, dunk the flour coated sausages into the batter. Gently tap off the excess, and then place into the hot oil. Carefully twirl the toothpick until it releases from the corn dog.
As soon as the corn dog floats, roll it in the oil so that all sides cook evenly. Remove from the oil when all sides are golden brown using a slotted spoon or tongs.