The so-called drying oils are more likely to produce a dark finish without the addition of any stains or tints. Plain old linseed, as you are using, is probably the worst in that regard, followed by Boiled Linseed Oil. BLO is not quite as bad as plain raw linseed oil because it is somewhat thicker due to the refining, and does not penetrate quite as deeply. Another characteristic of linseed oil is it's tendency to darken with age. With lighter pieces of walnut, these characteristics are exactly what some folks want. But with a piece of inherently dark walnut such as you have, you will end up even darker, and with grain that is obscured rather than enhanced.
Given the precautions and possible problems that others have described with different wood bleaching processes, I think I'd just use another type of finish for this particular gun. Some may think it heretical, but there are a lot of finishes that are much better than linseed oil on a gun stock.
