You can use an EDID emulator putting it between your Win10 system and the KVM switch which does not have full-time EDID feeding via DDC channel of the display connection. Use the EDID emulator...

Users said "KBM" switch, should it be "KVM" switch ?
Please connect system directly and test, don't connect via KVM switch first to see if you still can see the desktop or any video.
If video is...