One board tournament I work at a public library and we used to offer a monthly chess night, which is on hold right now due to lockdown regulations. We are planning to offer a small garden chess tournament outside the library with one chess set and maybe pre-registration to control crowd size.

What would you say is a good time format to offer? What tournament mode?

I was thinking to just do some "winner stays at the board, 6 challenges 15+0" kind of thing?
That'd probably be the best way- yes. A typical tournament would be difficult. Probably a blitz time control (something like 3+2) would be best, so games are over quickly. You'd also have to consider what'd happen if a draw occurs- my suggestion is to let the guy who won the game before that stay, or play another game. Also colours have to be decided- id say flipping a coin'd be best (other random selection alternatives are also good).