If using frozen shrimp, defrost over night in refrigerator. Rinse and drain well. Pat dry and place in bowl. Add marinade ingredients, reserving 1 teaspoon sesame oil for cooking. Stir to combine, cover and marinate in refrigerator for at least one hour but not more than 2 - 3 hours.
Prepare peanut sauce by combining all ingredients in a blender or food processor. Pulse until smooth.
Shred or julienne carrots and peppers. Thinly slice radishes, turnip, red onion and kohlrabi/jicama if using. Chop peanuts, green onions and cilantro and set aside.
Rinse lettuce and pull off 8 or 16 largest leaves. Use 8 leaves per wrap or double up lettuce for extra nutrition and more stable wraps. Spin dry or blot with paper towel. Arrange on serving platter.
Heat reserved 1 tsp of peanut sauce in a large skillet or wok. Add shrimp, along with marinade when oil is quite hot. Sauté quickly until shrimp are pink, turning or tossing as needed. Take care not to overcook shrimp, less than a minute on each side. Add about ¾ of peanut sauce to shrimp and stir to combine and heat through, about a minute. Turn off heat and add rest of fillings, except for green onion, peanuts and cilantro. Stir, toss to combine well.
Assemble wraps by spooning filling evenly into leaves. Top with green onions, chopped peanuts and cilantro.
Serve with extra peanut sauce drizzled over top.