Been using Johnson paste floor wax since I was 12 years old. A long time ago, it seems.
When the hunting seasons run late and there's a really good chance for inclement weather, I usually break the gun down before range time prior to the season, give it all a good gunge, and gun oil and grease in the guts, except for the locking lugs/shelf/latch...
As to the bore, I leave it completely dry. I use and keep a small roll of good electrical tape, give the barrel one layer across the end of the muzzle, and a wrap at least two layers thick around it to hold it on. I've yet to have the tape interfere with the bullet to the point that it changed my first round zero. Easy to remove, and it doesn't slip off, or rip, tear, and easy to re-apply.
Of course, now, I ain't on the coast, and even my trips to Alaska have been to the interior, so I'm dealing with light rain, or snow where I hunt.
If I was going to the coast, I'd probably do the same thing I usually do, and take the stainless Model 70 in synthetic stock.
Oh, almost forgot...I always have a small can of WD-40 in a pocket or the bag, works great to displace water, and it really really helps get wet kindling going quick when I need a fire fast.