I believe we found a work around for disabling the chat file transfer. It requires a small modification to one of the .js files that is used with web chat. What the fix does is essentially not hyperlink the sent file, so the agent can attempt to send a file however the end user can only see the file name and does not have the ability to click a link and access the file. Not an ideal solution but it does prevent file transfers.
Not sure if this would be helpful in your situation but if you're interested let me know and I'll send you more details.