Remote control of Cortana?

Should I be able to use my voice to control Cortana (Win10) on the remote computer within a TeamViewer session? So far I cannot get this to work. The reason I'm interested is that the user on the remote end is a quadraplegic and I'm trying to teach them to use Cortana to control the PC via voice.

I have tried using a TeamViewer remote control session, with TeamViewer audio/video VOIP on and the box for "share computer sounds" on the remote TeamViewer toolbar checked. The person on the remote ends sees and hears me, but this does lead to an audio feedback loop when I talk to my mic (a camera, not headset)  and the remote computer's speakers pick me up and port it back to me via the remote mic (also a camera, not headset).

I have also tried running a TeamViewer remote session, but keeping the box for "share computer sounds" on the remote computer unchecked. Then initiating a separate Skype video call between the 2 computers for the voice transfer. The person on the remote ends sees and hears me fine without any feedback, and I can control their computer using TeamViewer.

But regardless of the scenario used, Cortana on my local computer will respond to my voice, but Cortana on the remote computer never seems to hear me. Any ideas? Or is this just not possible?