I have a client that owns both a cat and dog, I usually only sit the cat as they take the dog with them. For the cat we held the meet and greet at their home, obviously, so they could go over feeding, litter box routine and show me where everything is kept. We held our initial meet and greet about a week before their trip, and made arrangements for me to pick up the key the day before they left. This client only lives one street away from me and I sort of knew them already as we both walk our dogs in the neighborhood so I was comfortable in going to their home. I have not had to deal with cat owners that I do not know yet but I too would be interested in how to deal with that, from a safety stand point. Dog Meet and Greets we do in a public place but with cats I would assume you would do that in their home.
Side Note... No matter where I do a meet and greet I always give two of my family members the address, time and name of the person I'm meeting.