If you can get the organization to switch to Debian, you could do it all with free software and manage the whole thing with Ansible.
I mention this because if the org is running Windows software that old, then current generation FOSS software is going to be a breathe of fresh air, by comparison.
It might not work if someone with a C title has a specific magical Windows package they want.
But even then, I would manage one or two Windows PCs (for a couple of C suite execs) by hand, than a full organization full. And you would save the organization a boatload of money.
There are multitude of OS & software in running. Some people still use DOS, but most of those were already upgraded - to windows XP. These machines are currently being replaced with Win10 ones. But due to some specific old SW there still need to be some DOS machines running, at least for couple upcoming years. Linux is sadly not an option for typical office workers, again due to some software in use. There's at least open source in places where possible with more (Firefox, Thunderbird, tightVNC, ...) or less (LibreOffice) success.
I haven't tried, but given how quirky it is (in house development decades ago with patches and hotfixes stuck to it over years) I highly doubt it would work. The main problem is that there's no will to use Linux in office environment...
We're at least running it on POS machines - about 150 openSUSE installs - where there's nothing fancy needed.
DOSBox runs on both Linux and Windows (and probably Mac too?); I was suggesting it since you might be able to replace the dying DOS computers with a modern system and just launch the legacy system as an application under it. (You might be able to do the same with a VM as well, but DOSBox came to mind first and may be easier to setup and distribute.)
Just a thought. If it's not useful, feel free to disregard.
I haven't tried to run DOS on Win10, but I haven't been able to get my old DOS programs to run on anything Windows XP or newer, myself. XP at least had some compatibility options to try. I don't think I've seen those options in Win7 or newer.
It will vary by program, but I've needed DosBox on Windows, as well as on Linux, for anything DOS based that I have run anytime recently.