Bring a large pot of water to a rolling boil over high heat. Add the noodles and boil just until tender (5-7 minutes). Drain the noodles and rinse briefly with cool water. Allow the excess water to drain away.
While waiting for the water to boil and the noodles to cook, prepare the rest of the salad. Peel the cucumber if desired. If the cucumber has a lot of seeds, cut it in half lengthwise and scrape the seeds out with a spoon. Cut the cucumber once more lengthwise (to make quarters) and then cut across into small slices.
Slice the green onion and roughly chop the peanuts. Combine the chopped cucumber, sliced green onion, and chopped peanuts in a large bowl.
To make the dressing, stir together the rice vinegar, sugar, sesame oil, salt, and crushed red pepper in a small bowl until the sugar is dissolved. Pour this mixture over the vegetables and toss to coat.
Add the cooled and drained noodles to the bowl and toss to combine the ingredients and coat in the dressing. Serve immediately or refrigerate until ready to eat.