Place meat in a container or a zipper-lock bag. Add soy sauce and sesame oil, and toss to coat. Refrigerate for 2 to 4 hours. Remove meat from refrigerator, and let rest at room temperature for 20 minutes. Place in a 250-degree smoker for 25 minutes or until meat is a medium-rare (about 135 degrees). Cool and chop meat into pea-sized pieces.
Heat olive oil and sesame oil in a large wok or skillet over medium-high heat. Add carrot and celery, and stir-fry for 3 minutes. Add chopped venison, soy sauce, and next 6 ingredients. Cook until warmed through. Transfer mixture into 4 bowls, and serve with lettuce cups.
To assemble the lettuce cups, spread a very thin layer of hoisin sauce on the center of a lettuce cup. Spoon a few tablespoons of the meat mixture into the lettuce, and add a drop or two of Sriracha for spicy heat. Hold the lettuce cup firmly, and eat from one end to the other.