Cook pasta to desired doneness as directed on package adding salt to water. Add frozen sugar snap peas during last 2 minutes of cooking time. Drain; rinse with cold water to cool. Drain well.
In large serving bowl, combine pesto and mayonnaise; blend well. Add cooked pasta, sugar snap peas, shrimp, tomato and onions; toss gently to mix. Sprinkle with cheese. If desired, serve salad on lettuce-lined plates.