|I never thought of swapping monitors while the OS is running as hot swapping, at least in the way it works with a USB device. I think the only risk you run is swapping in a monitor that's not compatible with the previous monitor's resolution or refresh frequency. But that's not likely to do any damage.|
I have noticed that sometimes a swapped monitor loses color and only shows a monochrome screen until the PC is rebooted. But again, no damage.
For the most part the OS doesn't care about the monitor. It just sets up the video card it's attached to and of course that's done when the OS loads.
I wouldn't worry about it. Think of all the times a monitor cable comes loose and is plugged back in while everything is running. If that caused problems we'd hear about it and I never have.
You're not really green until you're soylent green.