Once you've received a new beauty, a total disassembly, inspection, and general cleaning should be undertaken. I, personally, would never, ever shoot ANY new rifle I owned without a teardown. There's too much at stake. Once the metal has been cleared then a stock inspection is next. Since your rifles both have a finish remaining on them from what I see in the photos, a general cleaning might be in order. This is not to alter what's the stock looks like other than to simply remove a lot of accumulated grunge on the surface. While the car collector might never want to replace the old paint, he most certainly would not drive it around filthy. Same goes here. Begin with a surface wash of a solvent: either acetone or lacquer thinner. Neither one will affect the original finish on that stock but they will both cut through any petroleum based debris on the surface and in the grooves. Use a towel rag and, with appropriate pressure, bath the stocks (usually outside) until all the debris has been removed. Set the stock aside for about 20 minutes and let all the solvent evaporate. ( BTW I don't ever recommend mineral spirits. It's much too oily and doesn't cut debris away any where near as effectivel as lacquer thinner or acetone.)
Next, grab some Fantastic or 409 or some other water-based cleaner. Spray enough onto a clean towel rag to make it wet and once again attack the stock with it. This cleaner will remove any water-based debris that the solvent based material would not touch. Even after copious cleaning with solvents, you'll be surprised how much more grunge you'll get off. Again, this technique will NOT harm the original finish. Also, notice I said spray only the cloth, not the wood. That will keep the amount of water off the stock. The results will make this stock a bit lighter in color since the dirt has been removed. No problem. One other thing, however, and that's to inspect it carefully for any growing cracks or splits at this time. It'll be easier to see them. Gently but deliberately bend and twist the stock in your hand and watch for any cracks or splits that might appear under stress. If there are any, poke around the essays at the top of this forum for some guidance.
Now, after all that you reoil the stock. Find some
BLO
(boiled
linseed oil
) or some Tung Oil Finish. Rub the stock with it allowing it to sit wet under the oil for about 15 minutes. Then wipe the stock down and let it sit overnight. That will allow the oil to cure. Next day, wipe it again the same way. Since there's a finish on the stock all the new oil will do is provide another thin protective layer onto the cleaned surface and provide some protection to any areas that might not have an intact finish on it.
Voila! Nothing more needs to be done on either of those rifle. Reassemble after some oiling of your metal bits and you'll be good to go for a year. Once per year I recommend a wipedown of a cloth with some oil. You'll keep ahead of the shooting debris from the previous year and clean it at the same time!