Scooters in Santorini? And windsurfing in Naxos?

There are several windsurfing companies in Naxos. If you are staying at St George beach check out Flisvos it is att the extreme far end of the beach.

There is also windsurfing at Plaka beach.
Here is some info on all the kite surfing companies on Naxos.
https://www.tripadvisor.com/Attractions-g189431-Activities-c61-t197-Naxos_Cyclades_South_Aegean.html

Don't be surprised if you can't rent a scooter if you don't have a motorcycle license. The law changed, even for 50cc mopeds.