In a medium saucepan of boiling salted water, cook snap peas until bright green, about 2 minutes. Reduce to a simmer, and add shrimp; cook until shrimp are opaque throughout, about 1 minute. Drain, and rinse under cold water to stop the cooking; set aside.
Make dressing: In a blender, combine scallion whites, oil, lime juice, carrot, ginger, and cup water; blend until very smooth, about 2 minutes. Season with salt and pepper.
In a large bowl, toss together lettuce, bell peppers, scallion greens, snap peas, and shrimp. Serve salad with dressing on the side or drizzled over the top.
To trim snap peas, cut off stem end with a knife. Or, if the string is especially tough, snap off stem end with fingers, and pull string down the pod.