Reading there are only 40 taxis in Santorini. Should we arrange a airport shuttle to Vedema Marriott or chance it and hope for a taxi?
If true, that means there is more than 1 taxi per square mile. The island has an area of less than 30 sq miles.
I see no problem availability.
( No personal experience, but not a concern I have ever seen here)
I'm guessing that it would depend on what time of year you go. I visited Santorini in February, and of course, there was plenty of availability. If you arrive in high season, you may need to wait for a little bit of you haven't booked a transfer ahead of time.
Does your hotel offer shuttle service? I would ask before making arrangements. Taxi service from the airport is 24/7 and depending on how heavy you pack expect to pay a minimum of 20 Euros.
I just purchased Lonely Planet's latest edition (15th) that recommends www.santorinitransport.com with a fixed price from the airport or port to get to where you need to go.