Recompressing zip - integrity check

I have multiple large zip files and I would like to recompress them without unpacking them (I run the risk of ruing out of disk space). I am thinking of using advzip for that task.

However, I want to ensure that the compressed data is not corrupted in the process. How can I do that?

Obviously, hashing algorithms on the archive won't do here. What is my best option?

edit: Platform is CentOS 7