If we are traveling in Greece, including Santorini and Mykanos, April 2-24, 2019, is it best to reserve accomodations ahead of time or can we "wing it?"
You can wing it if you really want to. There are room finder businesses at or near the ferry ports, but if you arrive by plane you'll have to make your way into the main village areas to do your winging.
I think it's best to reserve at least one day ahead. There will be plenty of options, but I can't see any advantage to waiting to select a hotel until you're on an island, dragging your suitcases behind you.
You can still be flexible and "wing it" regarding where you go, and how many days to spend in each place. Just go to booking.com (or similar) in advance (you could even do that now), make a note of two or three options on each island that look good, and contact them the day before you arrive.
Perhaps it's just a weird timing issue of my chosen dates on Santorini, but I wanted to stay specifically at the highly rated Enigma Suites for our stay in March and I booked a long time ago. My dates have been sold out for weeks now. In randomly checking a few April dates, they are mostly booked for many of them. For me, great lodging makes my trips - so I don't leave it to chance.
For Santorini in particular at that time, I would recommend making reservations as soon as possible. Particularly if you wish to be in a particular area, like Oia for instance. (which is my preference)