Mix cabbage, carrots, coleslaw dressing, vinegar, soy sauce, and teriyaki together in a bowl; refrigerate until flavors blend, 1 hour to overnight.
Preheat oven to 350 degrees F (175 degrees C).
Heat sesame oil in a skillet over medium heat. Cook and stir ground chicken in the hot skillet until browned and crumbly, 5 to 7 minutes. Add stir-fry sauce, cover skillet, reduce heat to low, and simmer.
Form wonton wrappers into taco shapes and arrange between the cups of an inverted muffin tin.
Bake in the preheated oven until firm and lightly browned, 4 to 5 minutes. Spoon 2 to 3 tablespoons chicken mixture into each wonton taco shell and top with slaw.
