Hey there,
if the cats in neighbourhood are raggy looking, make sure your cats jabs and boosters are up to date. They're also something called Feline Aids out there now which attacks the immune system so just be careful you have everything covered. Not everyone takes good care of their cats not to mention all the feral cats around. So you need to do it.
I'm not sure a cat lead will endear them to their new home. Cats hate to be at someones elses beck and call! I think instead you could put them in the cat basket in the garden so they can have a look around for the first time, even for a few minutes. Then let them see you doing stuff in the garden. Cats love to see their owners working in the garden. and SarahW idea is a good one, let them out for a bit and then feed them. If they have some bed they use, put that in the garden for awhile too as it will be something familiar for them. And don't clean their bed etc before you move as it's important to have their scent on it when you move. I wouldn't worry too much, they know the hand that feeds them, so just be patient and be prepared for it to take time. Best of luck in the new home! mica