Preheat oven to 350 degrees F (175 degrees C). Grease a baking dish.
Heat oil in a skillet over medium heat; cook and stir squash and onion until tender, 8 to 10 minutes. Add water and simmer to soften squash, 2 to 4 minutes. Stir cream of chicken soup, sour cream, and Cheddar cheese into squash mixture; mix well.
Transfer squash mixture to the prepared baking dish; top with stuffing mix.
Bake in the preheated oven until cheese is bubbling and stuffing is browned, about 30 minutes.
