This is probably a much worse idea than the replies above, but you could also set up a server that runs RStudio Server and hook it up directly up to a router—instead of connecting to the Internet via a normal Wifi access point, the workshop participants could connect to your router and login to RStudio Server over the local network.
The biggest downside, IMO, is that your server would have to be able to support all the participants potentially running an analysis simultaneously. If it's exploratory stuff, that would probably scale well since participants would probably be sitting at the prompt 70 or 80% of the time, but if you're going to give them a big script or function to run and there's a good chance that they could actually all be tying up threads at the same time... maybe that wouldn't work so well.
Anyway, it's an alternative, in case the USB idea doesn't work so well! Note that although most modern systems boot fine from USB, you might want to consider having some portable R installations ready to go in the event that someone's system isn't configured for USB booting.