There is also an RDP app from Windows for Android and iOS, just so you know.
I wouldn't leave you high and dry!

If needed I can remote into production servers from my phone via VPN and RDP. It's all available.
Of course that's a last resort in my case, but the functionality exists.
A stylus comes in handy though when viewing a computer screen on phone .. I'd venture to guess the same applies to Teamviewer.

Be advised, free TeamViewer does have a limit. Use it enough and you'll find that out, and it would be bad if it hit its unexpected end during a show. I used it for a while and it suddenly said I needed to pay.
So RDP has that going for it; free (with OS) and no limits. Plus your connection never has to leave your network. I'm pretty sure Teamviewer goes through a server or two on the internet by design.
RDP doesn't need to if you don't need to.

If you are happy with Teamviewer, cool. It's a good product.
Just wanted to pass along what I know.

I do not work here, but the benefits are still awesome
Make your sound your own!