Much of the day-to-day work that we've been doing on Flash Player over the last decade is the invisible work of keeping up with the latest changes to browsers and operating systems. That work is no longer happening. At some point, it's almost certainly guaranteed to break, but I have no idea when that will happen, or why. The browser plug-ins have to contend with both changes from browser vendors (almost all of whom have dropped support for all browser plug-ins in the last month) and operating systems, but the projector/standalone player/executables still face risk from changes at the operating system.
Running old software in the modern world isn't a new problem (there are lots of banks and governments still running mainframe software from the 60s), and there are standard approaches to running legacy software. Converting your old computer into a virtual machine image for forward compatibility might be a cost-effective and workable option. Solutions like VMWare Workstation or VirtualBox are commonly used, but the specifics of that work are beyond the scope of what we're going to provide guidance about here. (It shouldn't be too hard to find an expert on legacy software archival to consult on this kind of work.)
Running in a virtual machine incurs overhead from the additional complexity (you're running windows on a computer built in software, which is itself running on windows running on actual silicon), so your expert will need to take some care in configuring it for consistent performance, and you'll want to thoroughly test it to make sure that it performs consistently as expected, etc. I definitely wouldn't want to find out about a crash or unexpected performance issue in front of an audience.
Regardless of the path you choose, there's work and cost involved. Do you spend time and money updating that show using modern technologies (and maybe taking it as an opportunity to refresh the creative), or on preserving it as-is? It's a highly situational choice that you'll need to make relative to your time, budget and interest.
Our support partner HARMAN might be an option, if this is a problem that you just want to pay a consultancy to handle. They work primarily with large enterprise organizations (banks, government, industry, etc) to repackage legacy Flash content as standalone applications with the intent of providing longevity for those critical applications.
You can read more about HARMAN here:
https://www.adobe.com/products/flashplayer/enterprise-end-of-life.html