How to add a shutdown script (not by using gpedit.msc or active directory)?

To anyone struggling to get this working, my sympathy. I spent many hours trying to figure out exactly which of the hundreds of changes gpedit makes are actually important. My tests were conducted on Windows Server 2016. These turned out to be relevant:

1. The values under:

   HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine\Scripts\[Startup|Shutdown]\0
   HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine\Scripts\[Startup|Shutdown]\0\0
   HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine\Scripts\[Startup|Shutdown]\0
   HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine\Scripts\[Startup|Shutdown]\0\0
   

2. The directories:

   \Windows\system32\GroupPolicy\Machine\Scripts\Startup
   \Windows\system32\GroupPolicy\Machine\Scripts\Shutdown
   

Windows uses those directories as the working directory for the scripts. Even if you don't keep your startup/shutdown scripts there, those directories need to exist.

Nothing else gpedit does seemed to matter. This includes many registry entries and the .ini files referenced in other answers. It's possible that some of the keys above are superfluous as well but I ran out of testing patience.

I got it working.

I added the script with gpedit.msc on one computer. I exported registry keys from HKLM\Software\Policies\Microsoft\Windows\System\Scripts and HKLM\Software\Microsoft\Windows\CurrentVersion\Group Policy\State\Machine. I also zipped the C:\WINDOWS\SYSTEM32\GroupPolicy directory.

On a different computer, I patched the registry with my 2 .reg files I exported earler on my first computer. I also unzipped my zip file to the same location on the second PC.

The script is running on shutdown and I see it in gpedit.msc. Everything seem to be good!