Heat oil in a deep fryer or wok to 350°F.
Measure milk in a 2-cup measuring cup then add egg. Mix to combine.
In a large bowl whisk cornmeal, gluten free flour mix, sugar, baking powder and salt.
Add wet ingredients to the dry and stir until combined. The dough will be quite stiff. Add a tablespoon of oil or more milk if it is too stiff to work with.
Insert a wooden skewer into each wiener stopping about half way up the wiener.
Using your hands wrap the dough around the wiener to completely cover it. Repeat until all the wieners are covered.
Gently drop the corn dogs into the oil 3 at a time. Cook for 3 minutes until golden brown. Repeat until they are all cooked.
If the oil goes above 350°F turn the heat down and wait. The corn dogs will brown too quickly at a higher temperature and the dough will not be fully cooked.
Drain on paper towel and serve warm with mustard and ketchup.