I hired a guy with a portable band sawmill to cut up a large English Walnut tree a couple years ago, and I can't believe how much weight the slabs have lost after less than two years of drying. I'm thinking the strength you lost from cancer treatment may be why those slabs seem heavier RHD45, and I hope you have a full recovery.
There is a lot of good advice above RARiddel, especially when it comes to proper grain flow and layout for a gun stock. English Walnut is the most desirable species among gun makers and stockers for several reasons, but may not be appropriate for restoring a gun that was originally stocked with black walnut. You should learn the difference between slab/plain, quarter, and rift sawing and what that means for gunstocks. Many wood sellers and wood buyers see some fancy figure, and become blind to all of the things that may make it very bad for a gunstock. The blank you are considering is plain or slab sawn, very straight grained, and as noted, the sapwood makes layout tougher. I'd advise passing on that one. I made several plexiglas templates that are large enough to encompass most 2-piece shotgun butt stocks, 2-piece rifle stocks, and 1-piece rifle stocks. With these, you can lay the clear plexiglas template on a slab or blank, and move it around to see if you can get the desired straight grain at the head, grain flow through the wrist, and the desired flow and figure in the butt. My templates are slightly over-sized in every dimension so I can be relatively certain that I can use a given blank. There are important considerations that determine whether your stock will be prone to split at the head or toe, break easily at the wrist if you should take a fall, or get damage from recoil, etc. You can see if you are likely to be able to get around splits or inclusions. And it's a whole lot quicker and better than the common method of drawing an outline of a stock on a slab or blank, because you can quickly move it or flip the blank over to make sure that the place which looks OK on one side is also good on the other side.
I bought a very full truck-load of dry black walnut slabs several years ago from a sawmill guy who was retiring. He also had hundreds of nicely figured walnut and curly maple gun stock blanks he had sawed out on his large vertical band saw. I rooted through them for several hours, and unfortunately, he knew nothing about correct grain layout for gun stocks. Easily 95% of them were nothing but fancy firewood. He couldn't understand why I had no interest in them, and bought all of those huge nasty rough sawn slabs for $10.00 apiece. Good wood has gotten very expensive, but you can still find some real bargains if you live in walnut country, and especially if you can buy green wood and have a place to properly air dry it to use perhaps a decade later.