I understand your client's predicament. I am working on the same thing, but with little priority at the moment so I can't present any solutions, just a few notes.
When I copy + paste an image from a saved OpenOffice document (doesn't work with an unsaved one) into a CKEDitor instance - I don't have MS Word here to test but I assume it works similarly - I get the following HTML inserted into the editor:

it might be possible to tweak a Flash or Java uploader in a way that this file can be fetched with very little interaction from the user. Being able to fetch files from the User's computer is a horrible security hole but it might be possible to at least pre-set an uploader to the temp directory directory.
However, the Canvas method that Gregory Pakosz mentions I find the most interesting, because this way it could be possible to store the image on server side silently, without any upload. The same security restrictions as in the above example still apply, though: The image is on a different domain, and thus cannot be read by a script on the page. One would have to find a way around that using browser settings or writing a custom extension.