To prepare sauce, heat oil in a small saucepan over medium-high heat. Add onion, 1 teaspoon ginger, and garlic; sauté 5 minutes or until onion is tender. Stir in soy milk, peanut butter, and juice; cook 3 minutes or until peanut butter is completely melted, stirring constantly. Remove from heat; cool completely.
To prepare marinade, combine wine, soy sauce, 2 teaspoons ginger, cornstarch, and 1/2 teaspoon black pepper in a medium bowl. Add chicken; toss to coat. Cover and marinate in refrigerator 30 minutes.
To prepare noodles, cook pasta according to package directions, omitting salt and fat. Drain and rinse. Set aside.
Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add chicken; sauté 2 minutes or until done. Add snow peas and carrot; sauté 4 minutes or until crisp-tender. Stir in peanut sauce, salt, and black pepper. Add noodles; toss well. Sprinkle with green onions.