Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, about 15 minutes. Drain and rinse thoroughly. Keep warm.
Mix soy sauce, water, rice wine, brown sugar, grated ginger, and cornstarch together in a mixing bowl.
Heat vegetable oil in a skillet over medium-high heat. Add red pepper flakes and chopped garlic; stir and fry for 1 minute. Add the shrimp and bok choy; saute until shrimp is pink and cooked through, 3 to 4 minutes.
Stir in tomatoes and soy sauce mixture. Cook until mixture begins to thicken, 2 to 3 minutes.
Place cooked noodles in a warmed serving bowl. Pour shrimp mixture over the noodles. Sprinkle with sliced green onions.