I have visited Fethiye twice now and both times in May. First time was at the end of May and it was warm enough to go in the water the second time was the Begining of May and it was a bit cool in the water.
The second time we stayed in Ovacik near Hisarounaru, it was the begining of May. The hotel had just opened up and we had a beautiful sunny week. The only thing I wish I had know at the time was that because Ovacik is in a mountainous area we were cold on an evening. In the summer months this would be ideal. If your hotel is at sea level you should be fine.Take a couple of warmer things for the evening.
Fethiye is a beautiful place to stay, it is very Turkish. Don`t just stay in your hotel visit the towns nearby. The rock tombs are a must. Calis beach is a great place for a day out go by water taxis is a trully amazing trip. 12 Island boat rip is a great day out, book it at the waterfront in Fethiye.
Oula Deniz is a fantastic beach, go there by dolomus and sit and watch the sky divers.
I am flying out tomorrow to Marmaris, I will give you an update on the weather when I get back if it will help you.