Cook the noodles according to the directions on the package. Drain and set aside.
Allow the noodles to cool slightly while you prepare the vegetables. Chop the bok choy. Cut the cucumber in half length-wise, then use a spoon to scrape out the seeds. Slice the flesh of the cucumber into half moons. Shred the carrots into thin ribbons with a vegetable peeler. Combine the vegetables and cilantro with the noodles.
In a small dish, mix together the vinegar, oil, soy sauce, and ginger. Season with crushed red pepper flakes. Pour the dressing over the noodles.
Sprinkle the sake over the shrimp. Grill over high heat for 10 minutes, or until cooked through. Serve the shrimp over the noodles.