Cut tofu in half lengthwise. Wrap each piece in a paper towel, place on plates and put a bowl on top of each to squeeze out water. Let stand for 20 minutes. Remove towels and cut tofu into 1-inch cubes.
In a wide, shallow bowl, whisk together soy sauce, lime juice, rice vinegar, sesame oil, sugar, ginger, garlic and chili sauce. Toss tofu in sauce and arrange in a single layer. Cover and chill for 15 minutes. Remove tofu, setting aside soy sauce mixture.
Bring a pot of water just to a boil. Cook noodles until just softened, 6 to 8 minutes or as package label directs. Drain noodles, rinse under cold water and drain again.
Combine noodles, reserved soy sauce mixture, carrots, bell pepper, scallions, water chestnuts and snow peas, tossing to coast. Add tofu; gently toss to combine. Fold in sesame seeds and serve.