Catswapping/ Can’t pick up new cat

Old man cat is a 12 year old spayed male who has been with my partner since kittenhood. New cat is a 3? year old stray that made us a part of her routine and is now full time indoors with us.

New cat is very sweet but predictably on edge. She has her own room and likes hanging out with me and my partner but she doesn’t like exploring the rest of the house even when old man is secured.

We’ve had her for two months and have made intermittent progress with feeding. They were eating about a foot away from each other with a gate and now I’m trying to keep it that way but move the gate so new cat will go into the living room.

My big issue - I haven’t been able to cat swap them consistently because I can’t pick her up and she’s very guarded about leaving the room. I’m worried this is impacting scent swapping. Has anybody else dealt with introducing older cats as such?

Edit to say I’ve watched all the Jackson Galaxy videos.