1. Bring a large saucepan filled with water to a boil over high heat. Generously salt water and return to a boil. Prepare an ice-water bath. Add snap peas to boiling water and cook until just tender, 45 to 60 seconds. Drain and immediately transfer to ice-water bath until cool. Drain again and pat dry; set aside.

2. Place crabmeat in a medium bowl and, using a fork, break it into bite-size pieces. Add peas and onion and stir to combine. Stir in vinaigrette; season with salt and pepper and toss to coat. Slice a small piece off each papaya half along the rounded edge and place on a plate. Spoon 1/4 of the crab mixture into each papaya half, garnish with lime wedges, and serve.