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Place shrimp in a resealable plastic bag. Sprinkle with Cajun seasoning and drizzle with olive oil; toss shrimp around in the bag to evenly distribute seasoning. Refrigerate for 1 to 2 hours.
Preheat a smoker to 250 degrees F (120 degrees C). Add wood chips according to manufacturer's instructions.
Place butter in a microwave-safe dish and cook on high until completely melted, 20 to 30 seconds. Stir in lemon peel, garlic, red pepper flakes, and black pepper.
Arrange shrimp in even rows in an 8x10-inch aluminum pan. Place thyme sprigs between each row. Drizzle butter mixture over shrimp.
Place in the preheated smoker and cook shrimp until firm and orange-pink in color, about 30 minutes. Try not to overcook as the shrimp will become rubbery. Serve immediately.