Preheat the oven to 200 F and place a cooling rack on a rimmed baking sheet.
Heat about 3 inches of vegetable oil to 360 F in a deep, heavy saucepan or electric deep fryer.
Mix cornmeal, flour, baking powder, sugar and salt together. Work the shortening into the dry ingredients with a pastry blender or fork. Add the milk and stir gently; stir in the egg until the mixture is smooth.
Insert a toothpick into the end of each wiener, leaving about one inch of toothpick exposed.
Dip each wiener by the toothpick into the cornmeal batter. Using a butter knife, spread the batter over the wiener so it is evenly covered.
Gently drop the wiener into the hot oil and cook for about 3 minutes or until golden brown.
Remove from oil and drain on paper towels. Transfer to the baking sheet with a rack and place in the oven while you fry the remaining corn dogs.
Serve the mini corn dogs warm with yellow or honey mustard.