Cook noodles according to package directions, omitting salt and fat; drain and rinse with cold water. Drain. Combine 2 tablespoons vinegar, sesame oil, 1 tablespoon honey, and sugar in a large bowl, stirring with a whisk. Add the noodles, onions, and cucumber; toss to combine.
Combine remaining 1 tablespoon honey, 1 tablespoon soy sauce, ginger, and peanut oil in a medium bowl, stirring with a whisk. Add chicken to bowl; toss to coat. Thread chicken evenly onto 4 (10-inch) skewers.
Heat a grill pan over medium-high heat. Coat with cooking spray. Add kebabs to pan; cook 12 minutes or until done, turning to brown all sides.
Combine remaining 1 tablespoon vinegar, remaining 1 tablespoon soy sauce, peanut butter, 2 tablespoons water, and sambal oelek in a medium bowl, stirring with a whisk. Drizzle mixture over chicken. Garnish with cilantro. Serve with noodles.