You will get the white stuff everywhere, no way to avoid that.
I mix the whiting powder with cheap rubbing alcohol to make a paste about the consistancy of mayo. Mix it up in a small jar that you can cap. Paint it on the stock with a small paint brush. It shouldn't run, but stick pretty much where you put it. It'll dry in a few minutes.
If you mix it up with acetone, it drys too quickly and crumbles off the wood as you try to build up the stuff.
Once you've got a coating built up where you want it, hang the wood somewhere and forget it for a few days and let the stuff soak up the oil. Don't mess with it after it drys as it's fragile and will crumble off the surface if you handle it. Just leave it alone and let it work.
It'll turn brown. Then it's time to scrubb the whiting off with a toothbrush. I do it over a trashcan outside. The dust is terrible and will get all over.
Recoat it again. Use the old stuff in the jar,,add some more powder and alcohol to it to mix it up again.
After the final time, I wash down the wood with warm water and the brush. You'll have to pick some of the whiting out of the corners of inletting but it comes right out.
I then bleach the wood with 'wood bleach',,,not laundry bleach,,.
Get it in crystal form in the home depot type store in the paint and stain dept. Comes in a plastic container usually. It's oxalic acid actually I think.
Mix up a few table spoons in a quart jar of water. Warm that up in the micro wave for 30seconds or so. While the stock is still wet from the washing you gave it to clean it of the whiting powder, brush the warm 'wood bleach' solution onto the wood and it'll lighten the wood and remove the stains at the same time.
It really evens up the color and gives a very nice base to start a finish from. Rinse the wood after using the wood bleach and blot the wood dry. Hang it again and let it dry for a day or two. Careful with it when it's wet as it will dent and bruise easily.
Some people quick dry it with a torch but I just let it dry on it's own. A torch will raise the grain if that's of an advantage at that point though. Careful you don't scorch the edges with a torch.
The wood bleach will sting your hands pretty good so you might want to wear gloves. Definetly some eye protection.
Whiting isn't fast but it does work. I usually do other work while the stock(s) are going through the whiting process. Otherwise it's like watching grass grow.