Combine first 4 ingredients in a medium bowl, stirring well with a whisk. Add shrimp to vinegar mixture; toss to coat. Cover and refrigerate 30 minutes.
Cook noodles according to package directions, omitting salt and fat; drain. Rinse with cold water; drain.
Heat a large skillet or wok over medium-high heat. Add oil to pan; swirl to coat. Add cashews, garlic, ginger, and chile to pan; stir-fry 1 minute or until garlic begins to brown. Remove cashew mixture from pan with a slotted spoon, and set aside.
Increase heat to high. Add sweet peppers, carrot, and salt to pan; stir-fry 2 minutes. Add shrimp mixture (do not drain); stir-fry 2 minutes. Stir in noodles and peas; cook 1 minute, tossing to coat. Return cashew mixture to pan. Add bean sprouts; cook 1 minute or until thoroughly heated, tossing frequently.