Is there a tool like Synergy for unified mouse and keyboard across multiple machines that does not require installing software on every machine?

I currently have a hardware KVM switch so that I can switch between controlling my personal laptop and my work laptop with one mouse and keyboard. Instead of only controlling one or the other at a time, is there a tool that would enable me to "switch" between my personal and work laptops without having to hit a physical switch? Ideally I'd like to be able to just move my mouse pointer from one screen to the other, click to bring a window into focus on either machine, and start typing in that window.

I'm aware of tools like Synergy, the only problem I have w/ that tool is I cannot install any software on my work laptop. I'm open to hardware or software solutions. Thank you!