Didn't you answer your own question? You need a windows vm, so install windows in a vm and connect your TV to it.
You might need to do a gpu passthrough for the hdmi cable to reach the windows vm video out.
Also, fair warning, controlling Netflix in a browser is probably impossible with your TV remote, so you'd need a mouse and keyboard. An android/google-TV box like the nvidia shield is much more user friendly in that regard.