High humidity works in your favor, for wood & stag. If humidity ever drops and stays dry (below 20% especially) for an extended period of time (weeks or longer), you'll want to watch the stag for shrinkage & warping especially. And some woods, but not necessarily all, will show issues too. I acquired most of my knives while living in Texas (Austin area) for 20 years. Fairly humid there, most of the time, with mid-day RH often in the 40% - 60% or higher ballpark, and rising to near 100% overnight (lots of fog & surface condensation outside). I moved back to my home state of New Mexico after that, which is usually much, much drier; RH often in the teens or single digits. Some time after moving back to NM, I noticed a couple of my stag-handled folders' covers were warped and lifting away from the scales. One of those knives' stag covers eventually came off after the ends of the covers pulled away (they were just glued on, not pinned).
I've never had any issues with bone covers at all, and I have a lot of them. It's pretty impervious to changes in humidity and needs next to nothing in terms of special care. If it gets scuffed up, it polishes very nicely with Flitz or similar polishes. But I've never needed to add anything to protect them from moisture or changes in humidity.
I have three walnut-covered folders from Case (1970s - 80s era). With the walnut on those, it gets to looking a bit dry sometimes. Maybe a couple times a year, when I clean up or resharpen them (on oiled stones), I oil the joints and blade just a little bit. The little bit of residual oil that is left on my fingers or rag gets wiped across the walnut scales evenly and left alone for a couple minutes or so. Then the excess of that is wiped away with a clean rag. That's all they've ever needed. As Bill said, don't soak them. Just a thin, light 'sheen' of oil applied a couple of times a year has worked for me. Many current-generation wood-handled knives seem to be in stabilized wood these days, and they need nothing special at all, unless you want to polish them occasionally.
