ambiguity - The department shredded all the files from the inquiry[,] 'which'/'that' contained embarrassing material

The department shredded all the files from the inquiry which contained embarrassing material.

After having read the sentence above, I was wondering if the department destroy every file, or only those with embarrasing contents.

Could one avoid ambiguity using a comma before 'which', like in A? Or is it better to this pourpose replacing 'which' with 'that', like in B?

A. The department shredded all the files from the inquiry, which contained embarrassing material.

B. The department shredded all the files from the inquiry that contained embarrassing material.