Have you not asked Thomas Cook? Its not as if you have a hotel to stay around.

I've used several different companies but haven't ever had night flights.
From my experience of others travelling with us they would probably transfer you to one of their hotels to hang around until pick-up time. They wouldn't (I don't think) give you a courtesy room but a lot of hotels have good facilities you could use and if they have a Turkish Bath within the hotel, there are usually showers etc that you can use free of charge.

One other option is for you yourselves to book in a boutique type hotel as a day guest where they will let you use the facilities. We were on a gulet for two weeks last year and in the middle of the holiday you are hanging about waiting for new passengers with the boat in harbour being cleaned so we booked into a small apart/hotel. I think it cost us about a fiver each but it was worthwhile as we used the pool, the showers, had lunch there and generally relaxed.

Feel sure if you ask your rep (not always useful) or the crew on board the gulet, they will be able to recommend somewhere you could go.