Soak wooden skewers on a shallow bowl of water for 30 minutes; drain. Heat a skillet over medium-high heat; saute sausage links, turning every 2 minutes, until cooked through and browned, about 6 minutes. Thread each sausage onto a wooden skewer. Whisk maple syrup, cinnamon, and 1/4 teaspoon cayenne pepper together in a saucepan over low heat until warmed, 2 to 4 minutes. Remove maple dip from heat. Heat about 2 inches of oil in a deep-fryer or large saucepan to 360 degrees F (182 degrees C). Line a baking sheet with paper towels. Whisk flour, cornmeal, sugar, baking powder, chili powder, and 1/4 teaspoon cayenne pepper together in a bowl. Add milk and egg; whisk just until batter is smooth. Pour batter into a tall water glass to 3/4 full. Dip each sausage into the batter, swirling and dipping to evenly coat. Place the battered sausages gently in the hot oil, 4 at a time; cook, turning every 30 to 60 seconds, until evenly browned, 3 to 4 minutes. Adjust heat as needed to maintain 360 degrees F (182 degrees C). Transfer corn dogs to the paper towel-lined baking sheet. Serve with the maple dip.