Do you know how to make a screenshot of the Windows desktop (and not the lock screen) while lock screen is active?
Technically it must be possible since for screen recording there is this solution that records a selected window even during an active lockscreen.
It should also be possible to trigger the screenshot programmatically (e.g. via a keyboard shortcut and/or via CMD). Otherwise any solution would do, be it a Windows- or third-party-tool, a registry hack, a script or whatever.
Alternatively, do you know e.g. a third-party lock-screen that doesn't show on screenshots?