To marinate the chicken, in a bowl, add the chicken and sprinkle in the salt. Mix until fully absorbed. Add the white pepper and rice wine, then mix evenly. In a small bowl, combine the cornstarch and water to make a slurry. Add the slurry and egg white to the chicken, then mix until evenly coated. Add the cooking oil and mix again to seal in the marinade. Marinate while preparing the remaining ingredients.
To make the sauce, in a bowl, whisk together the soy sauce, dark soy sauce, oyster sauce, hoisin sauce, water, and white pepper until smooth. Set aside.
To cook the noodles, in a pot over high heat, bring water to a boil. Add the lo mein noodles and cook for about 3 minutes until al dente. Drain and rinse under cold water to stop the cooking process. Drain well and set aside.
To stir-fry the chicken, in a wok over high heat, add 1 tablespoon of cooking oil. Add the chicken in a single layer and let it sear briefly before stir-frying for about 4 minutes until fully cooked and lightly browned.
To stir-fry the vegetables, in the same wok over high heat, add the remaining cooking oil. Stir-fry the onion, shiitake mushrooms, carrot, snap peas, and red bell pepper for about 30 seconds until fragrant and slightly tender.
To combine the lo mein, return the noodles and chicken to the wok. Pour in the sauce and toss everything together until evenly coated and heated through. Add the scallions and give everything a final toss before serving.