Make the peanut sauce: In a medium bowl, whisk together peanut butter, soy sauce, rice vinegar, honey, sesame oil, minced ginger, garlic, chili garlic sauce, and lime juice until smooth. Gradually add warm water, 1 tablespoon at a time, until desired consistency is reached. Set aside.
Prepare rice noodles: Cook thin rice noodles according to package directions. Drain and rinse with cool water. Using kitchen shears or a knife, cut noodles into 2-3 inch pieces for easier eating.
Assemble filling: In a large bowl, combine shredded chicken, cooked rice noodles, coleslaw mix, shredded carrots, chopped cilantro, and roasted peanuts. Add half of the peanut sauce and toss until everything is well coated. Reserve remaining sauce for serving.
Prepare tortillas: Warm tortillas in microwave for 10 seconds to make them more pliable and prevent cracking.
Assemble wraps: Divide the chicken mixture evenly among the 4 tortillas, placing filling in the center of each. Fold in the sides, then roll tightly from bottom to top, keeping filling contained.
Serve: Cut each wrap in half diagonally. Serve immediately with reserved peanut sauce for dipping and lime wedges on the side.