Sorry, but if your product is "IE / ActiveX -only" in this day and age, you are failing at IT, it's as simple as that.
Sure, but you can also pity the poor mugs who've been given the job of maintaining whatever it is that was bought from supplier XYZ in 2003 because "as it runs in the browser, it won't need anything installing". Along with the software required to use the machine that goes ping or can the read the health insurance card…
It's really quite amaying that in all the hoohah we had about browser choice, not one government ever got tough with Microsoft regarding the restricting OS releases to particular versions of IE.
As IE 9 - 11 share largely the same codebase, shifting to IE 11 shouldn't in practice pose too many problems. And, there is also the issue of whether such a server should really be open to the internet at all, but that's a separate issue.