Preheat smoker to 200 degrees F (95 degrees C) and add 1 cup wood chips to start the smoke rolling.
Liberally coat chicken wings with about 2 tablespoons Cajun seasoning.
Place wings directly on the grate in the smoker or in an aluminum pan with holes to allow airflow. Add more wood chips as needed to continue smoke. Smoke wings for 2 hours.
Combine butter, garlic, and 2 tablespoons Cajun seasoning in a large saucepan over medium-low heat; cook and stir until butter is melted, about 1 minute. Stir hot sauce into butter mixture; simmer, stirring occasionally, until sauce has thickened, about 30 minutes.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Preheat grill to 375 degrees F (190 degrees C).
Cook wings, 10 to 12 at a time, in the deep fryer until no wings are longer pink in the center and are lightly browned on the outside, 5 to 7 minutes. Remove wings from the oil with a slotted spoon, letting excess oil drain from the wings.
Place cooked wings on a baking sheet and liberally coat each wing with hot sauce mixture.
Place coated wings directly onto the grates of the preheated grill; cook until sauce has caramelized and wings are crisp, 2 to 3 minutes per side.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. The exact amount will vary depending on cooking time and temperature, ingredient density, and the specific type of oil used.