Rinse and thinly slice cucumber. In a bowl, mix cucumber, onion, and sesame dressing. Cover and chill at least 1 hour or up to 1 day.
Up to 1 hour before serving, layer napa cabbage and red cabbage in a large bowl (see notes). Pour marinated cucumber mixture over the top. Sprinkle with green onions, cilantro, and sesame seeds. Just before serving, mix well.
Sesame dressing: In a small bowl or 1-cup glass measure, mix 1/2 cup rice vinegar, 2 tablespoons sugar, 1 tablespoon vegetable oil, 1 tablespoon Asian (toasted) sesame oil, 3/4 teaspoon salt, and 1/4 teaspoon ground white pepper. Makes about 3/4 cup.