Wash squash; cut in half lengthwise. Remove and discard seeds. Place squash halves, cut sides down, in a 13- x 9- x 2-inch baking dish coated with cooking spray. Add water to dish to depth of 1/2 inch. Bake at 375° for 40 minutes or until squash is tender; let cool slightly. Using a fork, remove spaghetti-like strands; discard shells. Set strands aside, and keep warm.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add onion and garlic; saute 2 minutes. Add zucchini, and saute 2 minutes. Add mushrooms; saute 2 additional minutes. Remove vegetables from skillet, and set aside.
Coat skillet with cooking spray; add turkey. Cook over medium-high heat until turkey is browned, stirring until it crumbles. Add vegetable mixture, ham, and next 5 ingredients. Cook over medium heat until thoroughly heated.
To serve, spoon turkey mixture over spaghetti squash; sprinkle with cheese.