In small bowl, stir together peanut butter, ginger, soy sauce, vinegar, sesame oil, and cayenne pepper sauce; set aside.
Fill a 5 to 6-quart pot 1/2 way with water. Add salt and bring to a boil over high heat. Add noodles and cook 4 minutes. Add carrots and cook 1 minute. Add shrimp and snow peas and cook 2 minutes more. Reserve 1/2 cup pasta cooking water. Drain noodles, shrimp, and vegetables into large colander. Transfer noodle mixture to large bowl.
With whisk, beat reserved cooking water into peanut-butter mixture until well blended. Add peanut sauce and chopped cilantro leaves to noodle mixture in bowl and toss until evenly coated.
To serve, spoon into 4 large bowls; garnish each serving with a cilantro sprig.