Does Rick Steves have a list of private drivers for Santorini?
I don't know if Rick has a list, but we used Kostas on our trip and were very pleased with his services. https://santorini-private-guide.com/tour-guide-santorini/
I don’t know about a list, but I remember reading (in Rick’s guide I believe) to rely heavily on your hotel staff on the Greek islands. The comment was along the lines of how the locals all know each other, and the front desk will have a relative or a friend that they can recommend.
At any rate, I emailed our hotels several times during planning. For instance, I was able to give flight info and they set up our hotel transfers. They made dinner reservations for us. And they suggested a private guide. Might give that a try.