Unfortunately, homemade applesauce does not have a long shelf life even if it is kept in the refrigerator. Cooking the apples destroys microorganisms, but applesauce without additives spoils relatively quickly. You can prepare applesauce very quickly with a straining mill. This will give you the perfect consistency for your applesauce.
Here's a tip: use preserving jars. You can use them to preserve the puree for up to a year. Simply boil the filled jars in water at 90 degrees Celsius for 30 minutes. If the straining mill is not for you, you can also try using a straining cloth.