We just sailed on Edge in early May. 3 weeks ago. We too had a private tour booked. We were in Santorini ship time, 12 to 9. We left ship at 1pm to make our 2pm tour. It was close, but we made it with 10 min to spare.
Most of our time was spent waiting in line for cable car. Some of our cruisers hiked up, but they said they were exhausted afterwards.
We did a Flying Dress Photo Shoot, in which we toured the entire island by private Mercedes Van. The driver was awesome because he would climb dirt roads with the van, so had minimal walking to unbelievable views. We ended up with a few pics in which our cruise ship is in the background of the spectacular view.
One thing that I should note. We spent most of our day being pampered with private transportation, BUT, when we checked our walking APP on our phone, later in the cruise. We found out that we climbed 32 stories of steps alone. In Athens we went to Acropolis and the mountain a few miles behind it, and only climber 20 stories that day, for comparison.
But to be fair, our photographer recommended a restaurant that was quite the climb down to. But we were rewarded by having the entire covered balcony to ourselves, while being served great food and drink! The climb home from there was sections of stairs that went from 4 to 6 stories of steps on a single run. From the bottom, it looked even higher! My feet hurt just remembering.
One last thing……. You realize that Viator is a third party website? Book direct and have the confidence that you can get somebody on phone if tour is not there. Viator’s 800 number takes too long, especially if the operator is acting as a go-between with delayed or lost tour.