I'm in the VERY early stages of planning a trip to Greece. Not interested in mainland Greece or Athens (been there, done that), but instead island hopping on a small ship. We took a "cruise" last year along the Dalmatian coast with Katarina line and it was awesome. I say "cruise" since it was the exact opposite of a normal cruise - 20 people, small ship, great food at breakfast and lunch, swim stops, small islands - nothing more than a mobile hotel that moved you from island to island and provided food at breakfast and sometimes lunch before the afternoon in port. Has anyone done this sort of thing before? It looks like there is a line called Variety Cruises that is similar to what Katarina does - anyone have first hand experience with them or any other?
Our Croatia 20-cabin trip boat, the M.S. Monet, went out of business. But it was great. It's not precisely what you asked for, but Windstar Cruises has 120 and 320 passenger ships, power and automated-sail, that go from Athens to Instanbul. There are about 3 stops in Turkey.
The historic sailing ship, the SeaCloud (originally a wedding gift to Meriweather Post (of the cereal fame) from E.F.Hutton), offers a Greek Isles itinerary. But, unless you speak German, I would not recommend booking directly with them, but instead booking thru the various alumni groups that offer trips from time to time or via National Geographic. We booked directly, and only 12 passengers out of the 60something passengers were predominately English speaking. Fellow passengers all delightful, just a bit awkward at some dinners, because after the pleasantries, conversations were in German. The vessel is now German owned. But, possibly the passenger make-up varies by journey...you could inquire.
The sailing ship is absolutely lovely, though.
Other small ship options are Silversea and Seabourn, with ships that have 200+ to 400+ passengers. We've also traveled with both of those cruiselines, and both are excellent.
Star Clippers does cruises with stops in Greece and they are around 100-200 passengers in size. That line is all sailing ships with a mix of clientele backgrounds.
Marcus I do not think that you will find something like Katarina line for a Greek island-hopping experience. One very good reason, if you stop to think about it. Katarina just went along the coast, so could be a small vessel, 20 psgr + crew. However, to get to the islands you would long for, you need to be able to deal with the Open SEA ... and that means a larger vessel. Variety Cruises DOES offer interesting 7-day sails on a moderate size vessel -- Galileo for example, has 49 passengers. This page describes the better of its itineraries -- https://www.dolphin-hellas.gr/cruises-greece/variety-small-ship-cruises/7-day-jewels-cyclades_islands-cruise -- in my opinion ... it goes to smaller islands, and spends overnight in the ports of some -- rather than dragging you back on board and leaving before you can enjoy the sunset, as larger cruise ships do.
One word of caution -- choose your time of year carefully. When I read disappointed reviews of small-ship cruises, they're usually about the necessity to skip highly-anticipated stops, due to rough weather. Like King Canute it is well to realize that you cannot command the weather to do as YOU wish. That means avoiding the July-August-September period whan higher winds may make for rough seas. Late May or early June is the ideal time ... 11 of my 12 trips to greece have been at that time, and the sea can be like glass ... and for swims the water, while brisk is SO refreshing! Also, when you're on shore, things are lively but not crowded.
I have not sailed on Galileo myself, but have been at a port town seafront cafe when one of the Variety vessels was in harbor, and its guests came walking from the mooring right into restaurants. All seemed to be having a lot of fun.