Over the years, I've had only scaredy cats and I've found that the best way to get them into their carriers is this:
Lure them out by using whatever works (food, treats, or even just enlisting the help of your family to chase and grab the kitty-- traumatizing, I'm sure, but it works). Then, I put my cat into a pillow case so I won't have to endure the rath of their claws. I have my carrier already open and then I put the cat (in the pillowcase) into the carrier, close/lock the carrier, and wa lah!! The kitty can get out of the pillow case once it's in the carrier very easily. Not once has one of my cats ever been stuck in the pillowcase so that's nothing to worry about. The same method works for getting kitty into the carrier post-vet visit, unless your vet does it himself.
Best of luck!! This is certainly a tricky situation!