Hi Si hun
One thing cats are brill at and that's picking up your own stress. They have the ability to seance what you are feeling the same as dogs can so if you can try and not worry or panic yourself it will help.
I have read in Vicky Halls excellent behaviour books that if a cat is scared of something, trying to comfort them actually reinforces the fear and basically says to them they are right to be scared.
I have found this actually works!
My two lads hate the car and hate the vets,all my cats have done. My bridge babes used to be scared of the box as well but with my lads now the box has always been out for them to sleep in so Garf & Marl are not worried about the basket.
I used to sit in the back with them with my hand in the basket stroking them and they cried all the way, ears back and wide eyes. After reading that i was actually reinforcing their fear and saying to them Yes you have a reason to be scared by fussing them. i now sit in the front of the car and act completely at ease (need to feel this from inside) and ignore them and it works!
They are not so scared and don't cry even in the vets any more! It's like a kid being scared of a ghost or something you say to them na don't be silly
So a huge key is actually completely relaxing yourself, being positive, and dominant in a calm way and getting the job done with as little fuss as poss.