Wow. Why?
Blocking Google Docs is by far the cheapest way to prevent its use, even considering the downsides of a complete block.
Why would you bother to look for some awkward way to work with customer's sensitive data over the internet, if you're going to get fired for finding that way? The main goal is to prevent random people from storing data in unapproved locations "because it was easier that way". You can easily make it not be easier, that cuts 95% of the sharing, and then the only practical reasons to do so are clearly malicious.
Dropbox, drive, icloud, you can easily firewall all of that.