Cut an object by some of its faces


I have a box with some of the faces removed and a shell modifier.
When rendered you will see some of the outer faces and some inner faces.
The question is, how to use outer faces to hide inner faces?

I’ve tried using matte/shadow on outer faces but it will still show the alpha for inner faces.
The only workaround I could see, would be to assign a matId to outer faces and using compositing software to cut by it.
This seems to be a complex solution especially when having an atmosphere fog element pass.

Isn’t there a better way to make the outer faces be completely transparent (remove them from the object) as well as everything behind it that is a part of the same object?

Maybe you have a better idea for this concrete example:
I have a live action footage of a table which I need to explode. I therefore model the object and use thinking particles to destroy it. To composite those two things together I only need the debris that are flying away and the inner part of the table that is revealed. The table itself should come from the footage.