Are you travelling by car,caravan or motorhome ? as each is totally different,if car then they will be in thier 'travel boxes' anyhow ? same really as in caravan or motorhome,surely but at least if the doors kept shut you can let them out,with more room to do so,cats are weird creatures,i thnk they will get very excited if moved from one cage to another,better to keep them quiet 'in your own place' and say nothing ??unless you have too,because their in car,cant believe how strong a cat can be,you will not hold one,if they dont want it.
Italy -Greece can be a leasurely drive,more like a holiday than te other routes,especially if you take extra time,although a little expensive,if you have 'extra,extra time follow the actual coast road from Thessaloniki past Kavala,its stunning,the motorway passes everything and you see nothing but of course faster.
We always,when we have time,drive down to the coast near Kavala from Bulgaria (up to 3 hours drive) and 'wild camp' in our motorhome there,stunning...have a good trip .