People too shy to set in massage chair in public
How "public" is the event?
If it is in a workplace, ask for a conference room or unused office.
If it is not out doors (or not windy!), you can use a folding screen.
Some people are self conscious about their size or shape, in which case, having their back to a wall, rather than head in to the wall and their back (also, rear end) on full display might make them more comfortable.
However, think about that set up at the start of the event as they might be feel even more conspicuous if you change the set up just for them!