Spray a medium-sized casserole dish with nonfat cooking spray and set aside.
In a medium-sized saucepan, melt butter and then whisk in flour. Reduce heat to medium, and stir constantly. Then pour in the milk and chicken broth and raise the heat to medium high. Continue to whisk constantly until the mixture begins to thicken, about 3-4 minutes.
Once the sauce is thickened, remove from heat and stir in the cheddar and Parmesan cheese, stirring constantly until the cheese is completely melted. Season cheese sauce with salt and pepper.
In a large bowl, place cooked spaghetti squash strands in it, and pour cheese sauce over top. Stir in Greek yogurt. Then pour into a casserole dish and bake in the oven for about 20 minutes, until squash is heated through and bubbly. Serve immediately.