The short answer is yes, if you want to. Cooked squash peel is edible (and loaded with fiber). However, I have yet to try it. I prefer to peel the raw squash and then cut it into 1-inch cubes. I recommend you use a good vegetable peeler, such as a Kuhn Rikon. It is powerful enough to peel the skin. If you do not want to peel the squash prior to cooking it, you can roast or steam the squash, scrape out the meat, and then add it to the soup.