Remove and discard skin and bones from chicken. Cut chicken into strips. In a medium saucepan bring water to boiling. Break up each package of noodles (discard seasoning packets or save for another use). Add ramen noodles to boiling water. Remove from heat; cover and let stand for 5 minutes.
Meanwhile, in large bowl whisk together peanut butter, coconut milk, cilantro, lime juice, sugar, salt, and cayenne pepper until smooth. Add chicken, cucumber, and green onions to peanut butter mixture; stir to coat
Drain noodles; rinse with cold water and drain. In a large bowl combine chicken mixture and noodles; toss to combine.