Hi Milly-wig,
You don't really have much to be worried about. Most likely you will have to go through one of the specialist pet handiling companies, as most airlines will not let you ship animals directly. The size of crate is pretty generous for each animal, won't be accepted if it is too small, and will have to have provision for water.
Once in the crate they are delivered to the airline quite close to the departure time so won't spend too long in the crate. The hold is dark, but is fully airconditioned and heated and most animals are quite happy to travel and sleep most of the journey. On arrival they will be taken off and their condition will be checked and then fed and watered as required, though this will not really be a consideration for such a short flight. They will become slightly dehydrated as you do given that it is a pressurised/ airconditioned hold much as the cabin in which you will travel.
The only warning I could offer is that if Cyprus is not part of the Pet passport scheme, i.e. no quarantine requirement for returning to uk then I would think very carefully about taking them if you want them back in UK at end of contract. Having once put a dog through quarantine I would never subject one again to that ordeal.
Hope this has answered some of your concerns.