Avoid moisturizing soap in general when doing this, since they often have silicones, and that can leave a film. Dish soaps are less likely to have them, so it's a decent one to try blindly... or just read the label.

But yep, this is exactly what I do. Usually hand soap, but the stuff I get is just plain soap, no fragrance or moisturizer, so it rinses super easily. And when it's properly clean, the water leaves the surface dry and streak-free.