[nickjj]

You could always run VcXsrv to act as an X server.

Then you can launch GUI apps through your Hyper-V based VM (or any hypervisor).

It has seamless clipboard sharing that works out of the box once you enable the option.

I even went as far as running i3wm through VcXsrv for a while but ultimately gave that up since multi-monitor support didn't really work, but if you have 1 monitor it was actually quite usable.