Combine first 4 ingredients in a medium bowl, tossing to coat, and let mixture stand 10 minutes.
Combine broth and next 4 ingredients (through pepper), stirring with a whisk; set aside.
Bring 2 quarts water to a boil in a large saucepan. Add bok choy; cook 3 minutes or until crisp-tender. Remove bok choy from water with a slotted spoon; keep warm. Add noodles to boiling water; cook according to package directions, omitting salt and fat. Drain the noodles. Arrange noodles and bok choy on a serving platter; cover and keep warm.
Heat oil in a wok or large nonstick skillet over medium-high heat. Add fish mixture, carrot, and onions; stir-fry 3 minutes or until shrimp are done and fish flakes easily when tested with a fork. Add broth mixture, mushrooms, snow peas, and corn; bring to a boil, stirring constantly. Cook 2 minutes or until sauce is slightly thick. Spoon over noodles and bok choy.