Add all the shrimp ingredients to a food processor and pulse until well combined and smooth. Form the shrimp mixture into 7 equal sized 2-inch balls. Insert a wooden pop stick into the middle of each shrimp ball and form the ground shrimp into a shape similar to a hot dog. Place shrimp dogs on a cookie sheet and put in the refrigerator until well-chilled and firm, about 30 minutes.
For the corn batter:
Preheat deep-fryer to 350 degrees F.
While chilling shrimp dogs, prepare batter. In a large bowl, whisk together 1 cup flour, egg, cornmeal, garlic powder, sugar, baking powder and buttermilk.
Place the remaining 1 cup of flour onto a large plate. *Dredge chilled shrimp dogs into flour then dip into the batter and fry in the hot oil for 3 minutes or until dark and golden brown. Remove to a paper towel lined sheet tray to drain.
Serve with dipping sauce.
In a small bowl, mix together the mayonnaise, lemon juice, Dijon mustard, horseradish, and paprika. Place in refrigerator until ready to serve corn dogs.
Hold corn dog by the stick for the first minute of frying, until batter becomes solid, then fry for another 2 minutes.