Marinate the chicken. In a bowl, combine the chicken pieces with the stir fry sauce, sesame ginger dressing, soy sauce, and brown sugar. Let the chicken marinate for at least 30 minutes.
Make the wonton shells. Heat about 2 inches of vegetable oil in a deep frying pan over medium-high heat until it reaches 350°F (175°C). Gently fold each wonton wrapper into a taco shape or triangle shape without sealing the edges. Fry until crisp and golden, turning halfway through. Transfer to a paper towel-lined plate.
Prepare the slaw. In a bowl, toss the cabbage, shredded carrots, and sesame ginger dressing until well coated. Refrigerate until ready to use.
Cook the chicken. Heat 2 tablespoons of vegetable oil in a non-stick skillet over medium-high heat. Add the marinated chicken and cook until fully cooked and nicely caramelized.
Assemble the Chicken Wonton Tacos. Spoon about 1 to 1 1/2 tablespoons of chicken into each shell. Top with coleslaw, then garnish with fresh cilantro and serve with lime wedges.