For the bbq sauce: Simmer the apple cider in a medium saucepan over medium-high heat until reduced by half, about 10 minutes. Add the ketchup, apple cider vinegar, mustard, sugar, Worcestershire, paprika and dry mustard. Bring to a simmer and cook until thickened, about 30 minutes.
For the shrimp: Place the shrimp in a resealable plastic bag. Combine the oil, parsley, sherry, lemon zest, red pepper flakes, garlic and shallots in a spouted measuring cup. Pour the mixture over the shrimp. Seal the bag, squeezing out as much air as possible. Place in the refrigerator and marinate, 30 minutes to 1 hour.
Sprinkle the oak sawdust chips over the center of the bottom of the smoker and put the rack in place. Remove the shrimp from the wet mixture, do not dry, and place on the rack. Close the lid of the smoker and turn the heat to medium. Smoke the shrimp until fully cooked and pink in color, 10 to 12 minutes. Sprinkle the shrimp with salt and serve with the BBQ sauce for dipping.