The trick to stir-frying without oil is to use high heat, a good non-stick wok (or well-seasoned cast iron), and just enough water to prevent sticking and burning without boiling the vegetables. The water you add should be boiling off almost as soon as it hits the pan; the vegetables should never be standing in it.
Cut the tofu into 1/4-inch thick slices. Lay them out on a double-layer of paper towels. Top with another double layer of towels and gently press down on each slice with your hands to remove as much moisture as possible. Remove from paper towels and cut into tiny, 1/4-inch cubes. Place into a medium-sized bowl. In another bowl, combine the soy sauce, water, rice vinegar, and sesame oil. Pour over the tofu, stirring gently (I used my hands) to distribute the sauce without breaking up the tofu.
Cook the pasta according to package directions. Drain.
Heat a non-stick wok. Give it a quick spray with olive oil if you like. Add the tofu and cook, turning periodically, until lightly browned on all sides. Remove from skillet.
Add the ginger, garlic, bell pepper, and mushrooms to the hot skillet along with a tablespoon or two of water. Cook, stirring constantly and adding water as needed to prevent sticking, until mushrooms soften, about 1-2 minutes. Add the cabbage mixture, and continue to stir-fry for another 1-2 minutes, until just softened. Add the pasta, gently fold in the tofu, and season to taste with soy sauce and sesame oil. Serve with additional chili sauce on the side.