Separately, dissolve the yeast and sugar in warm water and let it sit until it becomes foamy, about 5 minutes.
Add the yeast mixture to the dry ingredients and stir until a smooth batter forms. Let the batter rest for 10 minutes.
Skewer the hot dogs and cheese sticks on wooden sticks with the hot dogs first and the cheese at the top, cutting the cheese shorter to fit the stick if needed.
Dip each skewered hot dog and cheese stick into the batter, ensuring they are fully coated.
Roll the battered skewers in panko breadcrumbs, pressing gently to adhere.
Heat oil in a deep fryer or large pot to 350°F. Fry each skewer until golden brown, about 3-5 minutes each. Drain on paper towels.
Dust with granulated sugar if using and serve with ketchup and mustard.