First, prepare the peanut sauce. Heat 2 teaspoons oil in a small saucepan over medium high heat. Add onion, 1 teaspoon of the grated ginger, and garlic. Saute about 5 minutes until onion is tender. Next stir in the soy milk (or regular milk of your choice), peanut butter and lemon juice until the peanut butter is melted, stirring constantly. Remove from heat and allow to cool.
Next prepare the marinade. Combine the wine, soy sauce, 2 teaspoons ginger, cornstarch and 1/2 teaspoon black pepper in a medium bowl. Add chicken pieces and toss. Cover and marinate in the refrigerator at least 30 minutes.
Cook pasta according to package directions, omitting salt and fat. Drain, rinse and set aside.
Heat a large nonstick skillet, or wok, coated with cooking spray over medium high heat. Add the marinated chicken. Saute, stirring often, 2 minutes or until no longer pink inside. Add snow peas and carrot and cook 4 minutes, stirring often, until tender crisp. Stir in peanut sauce, salt, and black pepper. Add noodles and toss until heated through. Remove from heat and sprinkle with green onions.