In a medium bowl, whisk together the soy sauce, ginger, honey, vinegar, garlic and 1 tablespoon of the canola oil. Add the chicken and let marinate for 15 minutes.
In the meantime, use a vegetable peeler to create ribbons from the carrots; there should be about 1 cup of carrot ribbons.
Bring a medium pot of water to a boil, remove from the heat and add the ramen noodles; let sit for 2 minutes, then drain.
Heat the remaining 1 tablespoon canola oil in a large skillet or wok. Remove the chicken from the marinade, reserving the marinade. Stir-fry the chicken in the hot oil until cooked through, about 5 minutes; transfer to a plate and set aside. Add the cabbage, onion and carrots to the skillet and stir-fry for 30 seconds. Add 1/4 cup water, scraping up any browned chicken bits from the bottom. Add the cooked ramen noodles, cooked chicken and reserved marinade to the skillet along with the scallions. Stir-fry until everything is heated through and uniformly combined, an additional minute. Serve immediately with sriracha and lime wedges.