Shave the daikon into ribbons with a vegetable peeler. Toss with 1/4 teaspoon salt in a colander; let drain in the sink, tossing occasionally, about 15 minutes. Meanwhile, shave the carrots into ribbons with the peeler.
Make the dressing: Whisk the ginger, vinegar, lime juice and 1/2 teaspoon salt in a large bowl. Slowly whisk in the vegetable oil and sesame oil until blended.
Toast the sesame seeds in a skillet over medium heat, tossing occasionally, until the white seeds are golden, about 5 minutes. Add 1 tablespoon seeds to the dressing.
Toss the daikon and carrots with the dressing and season with salt. Top with the remaining sesame seeds.