Flecto Varathane Number 66 OIL Finish. Easy to use, cheap, waterproof exterior finish.
There's no doubt that this is tough stuff and highly water resistant. But HWally is looking for something that doesn't give the stocks that "dipped in plastic" sort of look. Now sure, a thin coat can be rubbed on but I'm not sure that a rubbed on/rubbed off treatment will be as durable and as water proof. And the other option of the semi gloss being brushed on avoids the shiny look but it still has the "dipped in plastic" look.
HWally, from the description of the issues with the wood it sounds like it came to you with an oil finish. So if you are looking to keep that sort of look and feel then your answer is more oil. But use the right stuff.
I would say that your best option is a small can of the Polymerized Tung Oil from Lee Valley. I use this on my cowboy action shot gun which sees a lot of wet winter use. It's worked just great and the water beads off like you see off the feathers on a duck.
Second best but still fairly decent would be boiled linseed oil from the paint store.
The typical Danish oil is a mix of some tung oil and some boiled linseed oil with some solvent to thin it out. It works well for the initial sealing coats and for soaking into and sealing the end grain of the stocks. But for the rubbing on idea of the regular feeding coats you're far better off with one of the straight oils with no solvent in it.
BUT! ! ! ! An oil finish is always a work in progress. Any oil finish used outdoors needs to be maintained with a rubbed on then buffed off top coat at least once a year. And maybe two or three times depending on the amount of use and conditions. I tend to re-coat my shotgun and a couple of handgun grips about once every 6 to 8 months when I notice that the water does not bead off any longer. The nature of this is when fresh the water literally forms drops that run off. As it ages the water forms into sheets that run off with "dry" areas in between the various patches of sheeted water. Then when in need of a freshening up coat of oil you'll find that the water just wets the whole surface and stays on the wood. You'll want to try to catch it before that occurs.
If this is a seasonal hunting rifle the trick would be to apply a small dab of oil to a small wad of cotton cloth such as a shot gun cleaning patch and rub it over the stocks firmly to to point where you see the finish become clear and shiny again. Do this a couple of weeks before you go hunting to give it enough time to be sure it cures to a good hard film. If you can set it out on a warm sunny summer's day the PTO or BLO will kick off in an afternoon. The warmth and amount of UV light makes a big difference in the cure of the oil.
Note that I keep saying "cure". The finishing oils being discussed here don't actually dry like paint does. There's no solvents and it's not a plastic that is dissolved into such solvents. Instead it reacts with the oxygen in the air to polymerize from a liquid to a solid film. Which is why I keep saying "cure" instead of "dry".
A key factor is to be sure that you seal off any end grain. On rifles with one piece stocks you'll find end grain under the recoil pad and inside the action inletting area. Be sure that any end grain gets a good measure of any finish you're using. If there's nothing on it at the moment then Danish oil will penetrate deeper than the more viscous PTO from Lee Valley. Be patient since the end grain soaks up a lot of product and that means longer drying and/or curing times. The clue is the odor it has. If it smells like paint thinner it's still drying. If it doesn't smell like paint thinner in the case of pure oil take note of the odor. When this changes by a marked amount then it's kicked off and is good for use or re-coating depending on the condition of the wood.
If it's really bad I'd flood on a fairly wet coat and let the PTO or BLO soak in for a good few minutes. Then buff off the excess with a disposable rag or paper towels. Buff it off hard. You only want to leave what is IN the wood, not on it. If it's really bad it may pay to use the solvent thinned Danish oil for the first coat so it soaks in well. Apply and keep it wet for about two or three minutes then buff off the excess. After that use PTO or BLO for subsequent coatings and periodic feeding coats.
With the rags or paper towels don't wad them up and put them in the trash. The oil gives off a lot of heat as it cures in contact with the air and the rages or paper can burst into flame far too easily. I've seen it happen. Just lay the rags or paper out where it can cure off. When the oil is crusty after a few days it's safely inert and you can toss the stuff in the regular trash. I like to put this sort of stuff outside where it's dry but keeps the smell out of the house. It's bad enough with the guns inside.
