While I love a summer squash soup, I meant winter squash soup, which isn't that different from a sweet potato soup. But summer squash soups do not turn out like baby food, I promise!
Just leave out the cream. Soups that are creamy in texture (veloutes) don't actually have cream most of the time. The cream is just added richness, but the smoothness comes from cooking your vegetables until soft and then blending them well.
If you want a bit of extra richness, you can temper in some sour cream or full-fat yogurt at the end if you have them.