Since I work with a rescue group, new cats are sometimes brought in. I will usually give them their own food, litter, and space for 2 days. That gives them time to acclimate to strange surroundings. There is usually a little posturing and fuss at first, but I have not had any serious problems. They all find their place.
Thank you to you and all who gave tips answering my question. Your approach sounds very doable.