Stray cat needs to be vaccinated

I have a stray I feed and she sleeps in the garage. She tries to come inside but I have dogs and another cat. She has interacted with the dogs and they got along. I want her to come inside as she wants to but I don’t know how to vaccinate her as she still doesn’t like to be carried, have her paws touched and is still cautious when we pet her. Does anyone have any insight?? She also has a clipped ear so I assume she’s spayed.