Most of our classic gamers aren't tech-savvy enough to fully endorse Linux. If we can give them a boot-and-run alternative then they'll go for it, but we'll lose them if we make them learn too much of the Linux culture and lingo. They will learn more over time, of course, but this is the way to get them over the threshold.
Yes, it appears that a Puppy Linux distro would work best on a live USB stick. I've done a bit of research and found that Simplicity Linux comes with Wine built in -- a big plus for our audience. Simplicity's weaknesses wouldn't seem to be a problem for our purpose.
The issue of missing graphics drivers will probably be important. There's a way to install them persistently on the USB drive, right?