It very much depends on WHEN you are planning to go there. June to August is usually packed right across Greece, however, having been to the Greek Islands both in peak season and outside it, and you can always find someone trying to flog you a place to stay, it just might not be ideal!
I would have thought you'd be fine on Skopelos just turning up. about 7 years ago
Arrived with the morning ferry from Skiathos in beginning of July. Several scooters and cars where there to sell you rooms.
It's accepted in Greece to look in a room first and reject it if it's not to your liking...or start negotiating.
Stayed myself in Delphi Resort in Neo Klima on the Western side of the island. Rent a scooter in Neo Klima (less then 10euro a day) and you can drive to Skopelos 'city' in half an hour or less...
Advantage of Neo Klima is that you are in the middle of the island for small trips... about 4 years ago