I'd prefer something that doesn't leave a permanent hole in their router and require them to configure port-forwarding (like VNC) if possible. GoToMyPC looks OK but expensive for how infrequently I would use it. Wireguard and RDP would be one option, but probably overkill. Any other suggestions?
If the device is running macOS: Share screen via the Messages app[﹡]. Yes, it’s possible and it works well.
If it’s running Windows: Use Google Meet and start remote control from there.
(Teamviewer is another convenient option, but I would trust the above options to be far more secure.)
[﹡] https://support.apple.com/sv-se/guide/messages/icht11883/mac
And if you need to remote in you can do it through Chrome Remote Desktop.
Of course, you have get over Google trampling all over their privacy.