Sorry I meant to comment of ferries and forgot. Your have some options for ferries.
For us we want to get to our next island as soon as possible. We learned that on one of our early trips to the islands. The ferry hop from Paros to Naxos which is only a hour hop actually took up half the day. We had to check out of the hotel, Cthey want you gone by 10) Get to the ferry port. Hang around the port till the ferry arrives, an hour to Naxos and an hour to get to and check in to the Naxos hotel. We were on the beach by 2.
So your options are to take the first fast ferry from Santrini to Naxos. Without checking actual dates that ferry is usually a Seajet coming from Crete. It gets to Naxos around 11 AM. The seajets are very large fast ferries. They are stable in good weather and with a chop. We have never encountered a problem with stability at all.
Your second option would be the mid afternoon Blue Star ferry. Its a conventional ferry so not as fast as the seajet. It too is stable with lots of deck space to wander around (Seajets too have a deck at the back of the ship that can hold 100 people but thats a different experience compared to the freedom to wander around the Blue Star. ) The other difference is the Seajets is only in the Caldera for just under 20 minute. The Blue Star is in the Caldera for much longer so the views of Santorini are better. The problem for me is the Blue star depart mid afternoon so will not be in Naxos till around 5. So you are sacrificing 6 hours on Naxos by taking Blue Star.
Book your ferry tickets when you arrive on Santorini. Any local travel agent can sell a ticket. By booking just before the hop you will have the latest weather/Strike information so you can alter your plans if necessary.