Preheat oven to 350 degrees F.
Arrange wonton skins in single layer on a flat surface. Cut out circles using a 2-inch cookie cutter. Lightly coat baking sheets with sesame oil, transfer rounds to pan. Drizzle wontons with a little sesame oil, season, to taste, with salt. Bake until lightly browned, about 5 minutes. Let cool completely. The wonton crackers may be made several days ahead and stored at room temperature in an airtight container.
Blanch the snow peas in a large pot of rapidly boiling water for 1 minute. Drain well then rinse in cold water to stop the cooking process. Julienne the snow peas, radishes, and carrots, place them in a large bowl. Add sesame seeds, mint, and ginger. Whisk together the marinade ingredients in a separate mixing bowl, pour 1/2 the marinade over the slaw, toss to coat.
Remove the shrimp tails and discard. Split the shrimp in half lengthwise and place in a large bowl. Pour the remaining marinade over the shrimp.
To assemble: place a small amount of snow pea slaw on wonton cracker. Top with 2 shrimp halves, cut side down. Garnish with black sesame seeds and mint before serving.