https://m.majorgeeks.com/files/details/real_d … tch_for_me.html

Does that one help? It's not what you asked for, but it tries to "restore" the functionality of previous versions.
Perhaps this will bring back the checkbox, too.
Not sure, though. Haven't tested it myself yet. 🤷‍♂️

Following up on this. Restoring the DOS boot functionality to Windows ME does not affect this dialog, and it still gives warnings when running certain DOS applications.

The easiest way to test it is to run a game like Dungeon Master.

For the time being, I've switched back to Windows 98 specifically due to this annoying popup, as I want to run DOS games from a shortcut without having to deal with any of this nonsense. I suspect that there should be a way to restore this functionality by replacing some files or patching something, but I don't know how this dialog works or what files it accesses. Maybe someone with some debugging skills would have some luck investigating this further.

You could try asking on MSFN they do alot more hacking of 9x there.

Yes, I did this. No luck yet.

https://msfn.org/board/topic/183712-how-to-pr … ng-ms-dos-mode/

That's sad. I assume MS tried very hard to make Me appear independent from MS-DOS.
Me is essentially using MS-DOS as a bootloader/runtime here.

Another idea. Check out some beta versions of Me.
Perhaps earlier versions still have the dialog still intact.

Good luck.