It's a nice thing you are doing for these cats. My grandfather has three cats that he does the same thing for. Only one of them is allowed in the house and he is a a big baby. I can flip him over, gently drag him along the carpet by his back feet (closer to me for pets and attention, of course
), pick him up etc. and he doesn't even flinch. He won't let anyone else other my grandfather and me near him. The other two are younger, brother and sister, and will only allow my grandfather near them since he has been the one who feeds them and they trust him.