@Book_Wyrm it might help you to know that the ずに structure is much closer to Classical Japanese than to Modern Japanese, which is the reason you’re seeing the old negation stem of する (せ) instead of the modern negation stem (し) . It would make perfect sense to use し if ずに were a Modern Japanese form, but it isn’t. That’s why you tend to find ずに in literature and more formal contexts.
する changes to せ when adding ずに, which is also same when attaching it to ○○ざるをえない (No choice but (slightly archaic))
Though be sure to remember that using ずに does carry a more formal tone than ○○ないで○○