Cut the turkey wings into drumettes and flats; discard the wing tips. Soak apple wood chips in water for at least 30 minutes or up to 8 hours. Prepare a charcoal grill for cooking with indirect heat and bring the temperature to 250 degrees F.
Stir together the paprika, brown sugar, cumin, chili powder, garlic powder, onion powder, mustard, salt and pepper in a bowl. Drizzle the wings with canola oil and liberally coat with the spice mix. (You may not need all of it.)
Sprinkle the wood chips over the hot charcoals. Coat the grill grate with nonstick cooking spray. Place the wings over the unlit side of the grill. Close the grill lid and smoke the wings until they reach 165 degrees F, 1 hour 30 minutes to 2 hours. Remove the wings from the grill and let rest 10 minutes before serving.
Serve with barbecue sauce on the side, if desired.
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