Rereading your first post, it seems your more interested in not having the stock crack, than keeping the finish totally original?
But you can also ask yourself just what part of the finish is still original? What is there now, dirt, grime and all? Or just the color and whatever oil was used by the maker?
If it doesn't have any cracks now, I'd doubt it will start cracking at your place just because you're in a dry area. Just keep the gun inside the house and it should be fine.
If you want to put some oil on it, that shouldn't hurt anything. It will change the color a bit. But the dirt, grime, etc has changed the color a bit already.
I think your question here is to try to limit cracking, but not necessarily worrying about somewhat changing the color of the stock?
I've done restoration work on a lot of rifles over the years, and keeping the finish as close to as found has always been very important to me. But sometimes, like the one below, the color is the problem and needs to be adjusted some
to look better.
Pictures of your rifle would sure help.
John