Dewhiskering is the last step in one cycle of the grain raising process, but you'll want to raise the grain and dewhisker at least 3 times. The logic here is that you will eventually get the rifle stock wet in the course of hunting. When that happens and the wood dries, the grain will raise up like your chin whiskers in the morning. You don't want that, so before you put the BLO on it, and after you have done the final regular sanding (to 220 or 320 grit) you wet it, dry it, and use a fine sandpaper (320 or 400 grit) to lightly sand off those little whiskers of wood. I do the fast method, where I wet the stock and then use a blow drier to dry it. The more times you go through the process, the less likely that when you do get the stock wet, the grain will raise up. After all that, apply the BLO. It'll penetrate better if you warm it (be careful doing that. No open flame) and/or mix in a bit of Mineral Spirits for just the first application. I'd suggest you flood the wood with straight BLO for several days until it just won't absorb any more. Wipe it off after each application because you don't want it to dry on the surface. Then, if you are willing to put in a bit more work, put a few drops of BLO on your hands once a day and rub the oil into the stock. After all that, wet weather shouldn't raise the grain. But if that eventually happens, you can use some wet/dry sandpaper in 600 grit and with an ample puddle of BLO you can very lightly wet sand it as smooth as a baby's backside. Or you can use Johnson's paste wax instead of wet sanding and rub it in with OOOO steel wool. Personally, for the sake of water repellency, I use the BLO and very fine sandpaper for touch up purposes. And every now and then put a few drops of BLO on your hands and rub it into the stock. Keeps it looking great. You can skip the hand rubbing with oil if you just want water repellency.
All this is said with my assumption that you are reworking a military stock. If you're actually doing a fine walnut stock, there's even more you can do to make it look great with a BLO finish. Google up "hand rubbed Oil finishes", and I'm sure you'll get all the detail you want. If not, PM me.
I hope that answered your questions.