Using a julienne peeler, shred the daikon, cucumber, and carrot into thin strips. Place the vegetables in a bowl of ice water and let them soak for about 5 minutes until crisp.
Meanwhile, whisk together the mayonnaise, soy sauce, Japanese mustard, and sugar until smooth. If you don't have Japanese mustard, use horseradish or wasabi instead.
Drain the vegetables thoroughly in a fine-mesh strainer, shaking off as much water as possible.
Arrange the vegetables in a serving bowl, drizzle the dressing over the top, and garnish with the white sesame seeds and cherry tomato if desired. Serve immediately.
