Place a deep hotel pan or roasting pan over medium-high heat. Place 2 handfuls of soaked Applewood chips into the bottom of the pan and top with a perforated hotel pan or set a cooling rack over the roasting pan. Allow the wood chips to smoke.
For the marinade:
Combine the kosher salt, sugar, paprika, juice of 2 limes and drizzle of extra-virgin olive oil into a bowl. Add the chicken wings and legs and toss to combine.
Place the legs and wings into the perforated hotel pan or cooling rack set over the smoking chips and cover the pan with foil to smoke about 3 to 5 minutes. This will impart flavor, not cook the chicken
Meanwhile, place a cast iron pan over medium heat and add 4 cups duck fat and using a deep fry thermometer to monitor the temperature, allow the fat to heat to about 320 degrees F.
For the wing sauce:
Place a medium saucepan over medium heat and add the sriracha, apple cider vinegar, and honey (or to taste, depending on preference of sweetness versus spicy and vice versa) and place over medium heat to combine. Once the sauce is heated, taste and season with salt.
When the fat is heated and the wings and legs have smoked, add the legs to the heated duck fat and cook for about 4 minutes, being careful of any of the fat spattering. Once they crisp and brown, flip the legs and add the wings. Be careful of splatter when adding the wings and cook until brown and crisp, about 2 minutes. Flip the wings to finish cooking, about 2 more minutes or until caramelized and crispy on all sides. If desired, use a meat thermometer and make sure the temperature reaches 160 degrees F.
When ready, remove the legs and wings and place into the heated hot sauce and turn to coat. Add 1/4 cup unsalted butter and place into a bowl and stir to coat. Taste the sauce and season with salt and juice of 1 lime and a touch of honey, if needed or desired. Toss to coat evenly and set aside.
To a medium bowl add the radishes, celery, salt, cilantro, drizzle of extra-virgin olive oil, and blue cheese crumbles and toss to combine.
For each serving, plate 2 wings and 2 legs and top with some of the celery-radish salad. Serve any remaining hot sauce on the side.