Bring your offset smoker to temperature – You will want to maintain a temperature of roughly 250 degrees throughout the entire smoking process.
Prepare the shrimp – Place the shrimp in a large bowl and sprinkle with the Old Bay seasoning. With your hands, mix and work the seasoning onto the shrimp. Skewer the shrimp onto the wooden skewer. Place the shrimp on an oven wire rack.
Make the shrimp barbecue sauce – With a whisk, combine the shrimp barbecue sauce ingredients in a small saucepan and bring to a low simmer. Place the warm shrimp barbecue sauce in a small bowl.
Place the skewered shrimp on the wire rack onto your smoker – Smoke the shrimp for a total smoking time of approximately 45 minutes to 1 hour, depending on the intensity of your heat and the amount of your smoke. After 30 minutes, liberally brush the shrimp barbecue sauce on the shrimp, then flip the skewer over and brush again. Repeat this step one more time before the shrimp are finished smoking.
Remove the skewered shrimp from the offset smoker – Serve the shrimp on the skewer and let your guests pull the shrimp off the skewer for a fun and enjoyable dining experience. Be sure and have plenty of paper towels, as this will get messy. And have a bowl to throw the shrimp shells in too.