Decide if you want to fill the grain on the walnut or not before using the oil, its an aesthetic choice. Personally I like the grain to show most of the time but will fill it if I think the project will benefit from that.
For a hand-rubbed satin finish I too recommend the Chambers Oil. Applying it is a process and takes patience, there is work involved. Expect to work at it for two weeks or more according to how quickly it is drying between coats. Your stock sounds as if it is sealed now with those products you have already applied, so using the oil will be for final finish and top coating. The oil should work fine over the sealers you already have but before you begin with it be sure to rub out the existing finish (it must be DRY first) to level it and obtain as even a finish as is possible. One could use 400 grit paper, 0000 steel wool or 3M fine grade pads.
The process of applying the oil: Use fresh product. Using your finger or a small lint free cloth pad (1x1") apply a drop or two of the oil and rub it around until it covers as far as it will go and begins to "tug" or resist going further, wet the cloth or your finger again and move to an adjacent area and repeat, slightly overlapping the area you just finished. Keep doing this until you have the whole gun covered. At this point you will have some streaking and swirls, don't worry about them. Set the gun aside and allow the oil to completely dry. The trick is applying light thin coats as evenly as possible. Do not gunk it on!
Drying will be according the environment the gun is in, it could take hours or it might take a day or more. Be sure it is dry, or at least 90% dry before applying more oil. Once dry repeat the process described above, let dry once more. Applying these coats requires developing a "touch," but you will soon learn that.
As you apply successive coats a buildup will occur. For me after about the 3rd application I wait until the oil is completely dry and then go over the rifle with 600 grit paper wet with Mineral Oil, go with the grain using a light touch. This removes the swirls and levels the finish, you do small areas at a time just like when oiling. When finished with the paper wipe all the mineral oil off with a clean rag, t-shirt, etc.
You are now ready to apply more coats using the same method as above. You be the judge of when the finish is built to your liking. I find 6-7 applications generally result in the finish and look I like. Once you decide to end the oiling process you'll want to rub out the finish to level it all over, but you MUST allow the oil to completely dry first. There are many techniques for rubbing out a finish, some just do it with lots of elbow grease and the palm of their hand. I use Rottenstone and mineral oil applied with a 5x5" square of t-shirt cloth made into a pad by putting a small square of foam in the middle of the square, wrapping it in the cloth and tying it with string. I put some mineral oil in a shallow can lid, dip the pad in it and then dab a bit of the fine rottenstone on the pad and just like applying the oil I lightly rub in circles covering and overlapping one area at a time.
That is the way I do an oil finish, others probably do it differently.
dave
