Knoppix, at least, comes with samba installed by default, and I think it only needs a bit of setting up to get it to share its drives. Perhaps you could set it up on one system and save the profile to a usb stick that you can use to boot with on other machines. It might not be perfect, considering how varied people's computers can be, but if you set up a rather generic configuration you might be able to use it with most setups.
Another option would be to build your own customized live cd. I know there are webpages and scripts out there to help you set one up.