How can I stop someone from snapping the screen in a Connect Meeting?

You really can’t.

This is something that no applications can do without huge changes to the client computer (and why even the Disney Corporation watermarks their content)…if they can’t digitally control asset copying then nobody can.
The issue is that no matter what you do, the client can install other screen capture tools (heck, I have loads of them for just this purpose) and ultimately we can’t stop people using a camera and snapping the screen.
There is software out there to try to manage this, I have seen one that essentially ‘shakes’ the image or interlaces it, but nothing has ever been successful in the wider world…hence the watermarks you still see, even on photography asset sites.