To make the vinaigrette, combine the soy sauce and wasabi in a medium bowl. Whisk in the vinegar and sugar. Gradually whisk in the canola oil, then the sesame oil. Season with the pepper. Cover and refrigerate until ready to serve.

Place the tofu on a rimmed plate. Top with another plate and let stand to gently press excess liquid from the tofu, at least 15 minutes and up to 30 minutes. Pat the tofu dry and cut into 1-inch cubes.

Meanwhile, bring a large saucepan of lightly salted water to a boil over high heat. Add the string beans and cook just until crisp-tender, about 3 minutes. Drain and rinse under cold running water to stop the cooking. Cut into thirds. Cover and refrigerate until ready to serve.

Line a baking sheet with a double-thickness of paper towels. Heat the oil in a large skillet over high heat until very hot but not smoking. In batches without crowding, add the tofu cubes and fry, turning occasionally, until they turn golden, about 2 minutes. Add more oil to the skillet as needed. Using a slotted spatula, transfer the tofu cubes to the baking sheet.

Add the tofu cubes to the vinaigrette and toss with the vinaigrette (the tofu will soak up the dressing, so you need more than for a green salad). Add the string beans and red pepper and toss again. Use a slotted spoon to transfer equal amounts of the salad among salad plates. Sprinkle with the sesame seeds, along with the black sesame seeds, if using. Serve immediately.