Would you recon that gunmakers had the same climate issues during the 18th century and all of the 19th century? I would say proceed.
The question is: How did they solve them? Matching work to the seasons wasn't exactly an unknown concept back in the 18th century - Virtually all farmwork revolves around what time of year it is, after all. Living in the same climate and having some of the same humidity issues as Cory Joe (being too poor to run the air conditioner 24/7), I've learned that hafting axes in the spring-summer is a fool's errand and that such work is best done in the dead of winter, or the handle will loosen when the humidity drops. Probably not a good idea to just assume that they approached gunbuilding work with the same production-year-around mentality that we post-industrial-revolution types have today....
Having said that, I haven't done any wire work, so I can't comment directly, but I suspect that given the fact that no wood is actually removed in installation and the very small dimensions involved, that the wire would probably stay in fine - we don't generally see incisions in seasoned wood open up in winter, do we? It might be a bit more inclined to work its way out over the years, though. I, being a cautious soul, would probably do a test piece in the dog days of summer and wait until fall to do the gun, but I'm more than a little bit OCD about, well, a lot of things.