I can think of a way to do it:
Take the message typed, run it through text-to-speech, save the resulting audio file, and play it back in an obfuscated manner (Flash, maybe?) that makes it difficult to simply download the file.
Yes, it's horribly resource-intensive, it requires us to sell our souls, and it still leaves the possibility of recording outgoing audio (either with something like Audio Hijack or just by sending the audio out to something's audio in), but it's more or less what he wants! 
If it comes through my browser, I can make a copy of it. It really is that simple. There is nothing you can do about it. Forget any elaborate ideas. Really, I am serious, just forget them. You can write 2 million lines of code, you can write your own browser plugin, heck you can write your own
browser for all I care - it will take me a fraction of the time and a tiny fraction of the code to make a copy, and once I've done it, I can share it with everyone else.
