firdanse: What the others said.
I would suggest that you only stain the Walnut if it has areas of light heartwood in it and then, I would only apply it to the light wood areas to make them match the rest of the wood, but that's just me.
As you may know, I would suggest you use a water base stain. Water (or alcohol) based stains can easily be thinned with water. This allows applying thinned "washes" which allows you to control the amount of darkening easily.
Apply a coat, look at it in the sunlight, if it's not dark enough, allow it to dry and apply another coat.
Keep this up until it is as dark (when wet) as you want.
Oil base stains Really darken the wood on the first coat and then don't change the color or darkness much no matter how many additional coats you apply.
The original pistols which are still around were made of Walnut more often than not, and as Curly Maple was such a popular wood on longrifles, it tells me that carrying a Curly Maple stocked Rifle and a Walnut stocked Pistol would be quite Period Correct even if it was quite a bit darker than the rifle.
Before you stain the wood (if you decide to do it at all), you must take the stock outside on a sunny day and wet it with water. Only then will you know what the finished color of the wood will be because the wet wood will be Much Darker than it is when it is dry.
When you apply the finish, be it linseed oil or whatever, it will be the same color as the wood was when it was wet.
By the way, because we haven't heard from you, I assume your project is going OK?
Thanks for asking our opinions and let us know how it is going.