Cook noodles according to package; drain thoroughly. Whisk soy sauce, oyster sauce, sesame oil, sugar, water, and cornstarch.
Heat 2 teaspoons neutral oil in large wok or deep skillet over medium-high. Stir-fry chicken 4 to 6 minutes to 165°F in thickest strips. Plate.
Add remaining oil, cabbage, carrot, and snow peas; stir-fry 3 to 4 minutes until crisp-tender. Add garlic and ginger 30 seconds.
Return chicken with noodles; restir sauce and pour around pan. Toss 1 to 2 minutes until lightly coated.
Lift and turn noodles again to evenly distribute chicken and vegetables; serve immediately.