Depending on the sea conditions, you might be able to do something interesting with waves. Ignoring wind and air resistance for a moment, a craft like this will tend to slide down a wave, so if you are going the same way as the waves then propulsion is very simple. If you combine this with a sail then you could, if you are clever enough, use the difference in wave and wind movement to control your direction.

The Wandering Albatross [does something like this][1] to glide without flapping its wings. Your islanders are not going to do exactly that, but they will probably have related techniques. The simplest thing would be to use a sail to move sideways along a wave, using the trough of the wave a bit like a keel, thereby going to the left or right of the wind and wave direction. I don't think you could tack like this though.


  [1]: https://movementecologyjournal.biomedcentral.com/articles/10.1186/s40462-018-0121-9