1. Place noodles in a large bowl and cover with boiling water. Let sit until tender, about 10 minutes, then drain and rinse with cold water; set aside.
2. Meanwhile, to make the sauce, whisk peanut butter, chili sauce, warm water, soy sauce, and lime juice in a medium bowl until smooth; set aside.
3. Pat shrimp dry with paper towels and season with salt and pepper. Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat until shimmering. Add shrimp and cook until edges begin to brown, about 2 minutes. Stir and continue to cook until shrimp are pink and cooked through, about 1 more minute; transfer to a plate.
4. Add remaining 2 teaspoons oil to skillet and heat until shimmering. Add scallions, carrots, and pepper and cook, stirring frequently, until vegetables are just tender, about 3 minutes; reduce heat to low.
5. Add shrimp, noodles, and sauce to skillet and cook, tossing with tongs, until noodles and shrimp are heated through. Divide noodles among four bowls and sprinkle with peanuts and more scallions. Serve with lime wedges.