No and no. Tor is not magic. It is just a way to conceal your IP address.
Who else tried to do something like what you describe? Snapchat.
Snapchat is proprietary software running on largely proprietary platforms. They should have a far better shot than you, but they hardly succeeded.
I just searched for “snapchat screenshots” and this was the top (relevant) result: https://fossbytes.com/how-to-take-screenshot-on-snapchat/ It is a good post, describing many techniques to copy Snapchat posts without being detected.
All of these techniques, and others, apply equally to what you describe.
Basically, if you do not control your users’ computers, and you send information to those computers, you cannot control what happens to that information. And even if you do control those computers, you cannot stop your users from pointing their own cameras at their screens.