This isn't a you problem it's an organizational problem that isn't going to be fixed by doing things half-assed. So if it were me and I couldn't get approval then I wouldn't do anything and fail the inspection. (Communicate that up the chain so you have it in writing)

I would hope that wherever you work has the ability to review and approve software to be used on your systems.
DOSBox is not for production purposes and is only for usage for games because games are not critical so bad things may happen when used for other purposes.
Typically vmware, virtualbox, kvm, qemu are recommended in these cases as long as they are approved.

IMO,
If your radio requires DOS to program it then it's a simple matter of booting DOS on a physical system that has a serial connection or a serial PCI/PCIe card and doing what you need to do as long as you are approved to do so on those systems.

A lot of relatively modern corporate systems from the likes of Lenovo, Dell etc still come with serial ports, so it may be worth recommending to your management chain that they purchase a something like that. A suitable technical sales person at one of those big brands should be able to advise a model you can boot Dos on with a real serial port.

It sounds like this is essential for maintenance of your radio system, so the right tools need to be in place.

For anything work related I would not try to bodge it (you don't want the issues to land on you if there are problems down the line), and that includes buying second hand or used kit.

I have similar conversations in my line of work where researchers try to keep expensive lab kit going indefinitely... When things break they inevitably want to try and fix things on the cheap either attempting to make repairs themselves or by non approved parts (which could be anything from a fuse to a motherboard).

That's all well and good trying to get things done cheaply, but when that repair fails and ruins 6 months of sample data, the manufacturer refuses to service the machine due to nonstandard bits, or the faulty repair then takes out several hundred K worth of instruments, well, that cheap repair is no longer cheap!

Interesting suggestions. Thank you none the less. I am co-owner of the company so I can pretty much do as I choose. I have now come into possession of an old Dell Latitude with windows XP installed on it and it has a serial port. I truly thought I scored! Well, while trying to boot from the provided USB stick, which holds DOS and the kenwood DOS program, I get I/O disk error. When going back to the guy who sold me the cable and included USB stick, he stated is needed to be Windows 95 and Windows 3.1. Here I thought I was in business! Ugh....

Megatron-UK, I am just trying to get it to work. This stuff is old so not trying to go any "cheap route" as you say. My goal is to get it to work, that's all. And DOS freak, failing the inspection is not an option. My business depends on it. I will make it work, somehow, someway. It will come together.

I appreciate, the comments, and thoughts. Keep them coming! Especially now that I have a machine with a serial port. Thank you.

If you have a machine with a serial ports, then you could try booting from either a dos boot floppy disk or Dos usb memory stick (freedos supply one). You probably don't need to format and reinstall.

I assume the Comms software is small enough to fit in a floppy?

I'd go the FreeDOS route. It will run natively on your Latitude.

So the program runs in DOS, and when you say mount, do you mean run an .exe file ? If so, then perhaps FreeDOS is the way as suggested. You could burn it on a CD and run it in a live environment, have the USB with the programming software plugged in as well and mind the drive letter assigned to the USB drive. Then, run the program executable that's located on the USB drive.

All this sounds great! I wish I knew how to do it. This is all so foreign to me. Hoping the guy who sold me the cable can assist.

So the software to program the radio needs to be executed in DOS in order to function. The software package has an executable file to run it, something like "setup.exe" , where "setup" can have a different name.
In order to run it though, like we discussed, requires you to run in in DOS. I think the simplest way to achieve that, given that you do not have a machine that can run DOS natively, is to get a software called FreeDOS that can be downloaded off the internet, burn it to a CD and run it "Live" , as in without the need to install it on the hard disk, just insert the CD in the CD ROM and make sure you boot off the CD ROM. You might need to go into BIOS and ensure CD ROM is selected as primary boot device.
Once you boot off the CD ROM into FreeDos, if your laptop has a Floppy disk and the software to program the radio fits on that ( and I think it does), then you simply copy the software to floppy and run it. If no floppy drive available, then a USB should work also.
If this sounds too complicated then perhaps ask someone to assist you, maybe a PC shop can help.
There might be other ways of doing it, but this is how I would try it if I was in your shoes. Good luck.