MArk, just because they are not fat doesn't mean it is OK to feed them - there could be a medical reason why she is thin, and you could be making it worse. Sorry, but it is one of the things I really hate, as that is why i struggled so much with Ginger, my neighbours were happy to feed him, as they do all the neighbourhood cats and dont take any notice of owners asking them to stop.
I Think it would be easier with a dog, as long as you can take them for a decent walk that is, and it is also easier to fill them up with vegetables (tip a friend has been given by the vet to help her Shih Tzu).