Well grans cat will probably already smell your cat on you and your cat probably smells gran cat when you come home but I suppose there is no harm in taking a blanket or something from each and swapping them. It’s not something i know much about except in the case of doing it for comfort reasons with something that smells of the owner so I’m not best placed to advise!
the truth is you won’t know until you bring gran cat home but I think if you can keep them separately for a couple of days so they can both sense each other but can’t get to each other.
maybe gran cat in the bedroom where its quieter from the living noises but go in and sit quietly but semi regularly so gran cat has the chance to be around you and maybe be comfortable enough to come out from wherever it decides to hide (which it probably will for the first while)
when they get introduced they will probably hate each other but as long as they aren’t literally hurting each other and properly biting etc just let them prowl and growl and occasionally swipe at each other as that is how they will decide on their relationship. Although if one aggressively continually chases the other all the time that can be an issue so maybe step in to cut that behaviour a bit. Basically it’s ok if they argue and a bit physical with each other but not to the point of hurting each other or allowing one to really bully the other.
keep their food separately as in not next to each other and try to be strict about not letting them steal as one may use it as a dominant thing, which in turn can cause the other one to be too scared to eat for fear of getting attacked as they don’t feel it’s their own anymore.
the litter tray separation is important but keep an eye one doesn’t use both (like the food bowl) as sometimes cats will use both to be dominant but the result can mean the other starts toileting in the house elsewhere and not use the tray at all but if it starts then because that area will smell it can be hard to break it using that area over and over.
if they or even one is it might be easier as it means they get space from each other and feel ok when they are sharing space.
the truth is it is going to take time not days but probably weeks and it may need some management but there’s a good chance that even if they never become best friends (although they might) they could happily co exist (the friend I mentioned is in a one bed house so not a huge amount of space either but one is an outdoor cat during the day)
my advice would be to have a good nose online there will be a lot of information about how best to introduce a new cat and advice when a particular issue comes up!