I would imagine you would need a few more to rent a boat privately, maybe you will meet up with some people while here and can share the boat/cost.
if not i can certainly recommend jerryboat if you search on the forum you will find lots of people been with jerry a number a times like us, a great guy with a small boat only taking around 14-18 people out at a time, his wife cooks fab food, and then a bit of fishing on the boat trip.
you will see Jerry walking along the front in Calis most evening taking bookings, if not pop along to the harbour in fethiye and look for his 2 boats around 6pm we usually catch him there, and book with him there.