To turn regular chicken legs into lollipops, you'll need a sharp knife and a pair of kitchen shears. Start by making a cut all of the way around the leg just below the knuckle, cutting through the skins and tendons using either a sharp knife or a pair of kitchen shears.
Push the meat down to the large end and pull/cut the remaining skin and cartilage off the knuckle. You might want to also remove the tiny bone right against the leg. Remove this bone with your fingers or the shears, and trim away the tendons sticking out the top.
Season the chicken with the Cajun Shake. Wrap the bones of the drumsticks with a small piece of aluminum foil to keep them from turning too black. Let the chicken sit for an hour in the fridge to allow the flavor to permeate.
Start the Traeger on Smoke with the lid open until a fire is established (4-5 minutes).
Place the chicken lollipops on the grill grate and let them smoke for 30 minutes. After you remove the chicken, turn the temperature up to 350F and let preheat, lid closed, for 10 to 15 minutes.
Place the stick of butter in a baking pan or aluminum pan and put on the grill to allow the butter to melt while the grill is coming to temperature. (The butter doesn't need to cover the chicken. It just keeps the drumstick moist and of course gives it a little added buttery finish.)
Arrange the lollipops in the pan with the bones sticking up straight. Let the chicken cook for about 40 minutes or until the internal temperature registers 165F on an instant-read thermometer.
Meanwhile, warm up the barbecue sauce in a small saucepan on the stove over low heat. If you want it to have that Louisiana kick, add in a few squirts of the hot sauce, to your taste. Once it starts to thin, turn down the heat to just keep it warm. If the sauce needs to be thinned, pour in a little bit of the butter used in the pan until it reaches a thickness that is thick enough to adhere to the drumsticks but not gluey.
Dip the lollipops into the barbecue sauce so that it is completely covered. You can also brush the barbecue sauce on the bones if you want a uniform look and sheen on the lollipops.
Increase the temperature to 450F. Place the chicken directly on the grill grate and cook until the internal temperature registers 175F, about 10 more minutes. Keep an eye on the lollipops to make sure that the glaze doesn't burn. You're looking for that perfect caramelization of the barbecue sauce on the outside with a crisp skin to give a little texture.