Documents from the Keynote application cannot be used natively on Apple TV, but can be shown on TV through AirPlay. If you can’t bring your computer to the same room, then one option is to remote control your Mac from the Apple TV. An app called ‘Remote, Mouse & Keyboard’ promises just that, not using the standard AirPlay controls, but something of their own making. Not free though.
- Remote, Mouse & Keyboard app - App Store preview - Apple [subscription model]
- Remote, Mouse & Keyboard Pro app - App Store preview - Apple [one time purchase]
https://cherpake.com/apps/remote-mouse-keyboard/
These apps for Apple TV also need a companion app on the computer to make this work.
I can confirm that it works before paying, but perhaps not all features. I am not a regular user of this, so I wouldn’t be able to answer in-depth questions on this app.
I guess having a laptop would be an advantage over a not-so-portable computer, for this type of use.