Is it normal to have night sweats with no fever four days after an appendectomy?

Talk to your surgeon: May or may not be a sign for concern. Fever may be blunted if taking medications for post-operative pain control that contain anti-inflammatory and / or analgesics (e.g. Ibuprofen, motrin, naprosyn, (naproxen) aspirin, acetaminophen, apap, etc.). Mention this to your surgeon since it could be an early sign of peritonitis.

Postop sweats: Walking opens up the base of the lungs and sometimes can cause sweats, an early wounf infection or resolving peritonitis from the appendix can cause sweats for a week or more. Check your temp and call your doctor if fever greater than 100 or wound redness and pain which could happen about post-op day 5.