Some sort of remote desktop solution is about all you can do if you don't want to get a switcher or move the cable.

Cygwin on Windows can be run as an X11 server, so that GUI apps on your Linux box can be displayed on the Windows desktop across your network. Responsiveness will be reduced a little, but X11 works decently over a network.

Or you can run a VNC server on your Windows machine and just use it via a VNC client.

Neither of those solutions are very good when the remote side needs hardware graphics acceleration, though.