Cyanoacrylate works by flowing into the wood through capillary action and binding the wood fibers together. It's great for porous wood like balsa but not so good for walnut. Also, if you get a little on the wood finish you'd have to refinish the stock.
Here's what absolutely worked beautifully for me, on a Remington .458 win mag rifle stock: Contact Brownells. They offer a cyanoacrylate product that is especially "runny". I can't remember what they call it. Might be "Hot Stuff"..??? When I bought it, they also offered disposable applicators for this product that taper to a VERY fine tip so you can put the glue where it needs to go, and keep it from where it doesn't need to be. Careful masking off of the non-crack area is also a good idea.
Flex the stock enough to open the crack a little so the glue can get into it, apply all it will take, then release the tension holding it "open", and wrap the whole thing tightly with surgical tubing. Leave overnight.
I have been reading a lot about this glue type lately and the more I read the more confused I become. From what I've read there are three consistencies, water thin, medium, and thick. Obviously the wider the cracked area the thicker glue you need. Comes in clear and black from what I've seen and even found a kit where you can color it to match your wood.
I have used and a gunsmith friend also use it. Fly tying glue I think the brand is goat tough I got it at cabelas in the fly fishing section it works well just leave it clamped overnight till it dries. The best stuff I've used is brownells accuglass
For what it is worth I have repaired some badly broken stocks with it that years later are fine. This includes several that were broken through the wrist or had sections broken off at the toe. The glue line becomes nearly invisible after careful sanding down to the original finish. It also works well to repair chips in epoxy finishes. Dale.
The thin stuff that Brownells sells is specifically made for wicking into stock cracks. You obviously have to use a little at a time and apply it multiple times to eventually fill the crack. I think they may even sell fine point applicator tips for this operation. Cyanoacrylate adhesives cure in the absence of air which is why they dry quickly when you press two parts (or your fingers) together. In an open crack in wood, it will take surprisingly long to dry hence the multiple applications of a small amount approach. Good luck.
Thanks guys. I am not sure I described the crack accurately. It's about 4" long, not open and doesn't need filler. In any case, taking all of the advice together I came to what I think will work. I was able to get some very thin cyano glue from a friend and after seeing the crack his advice was very similar to many here. I opened the crack a little, used a toothpick as an applicator, filled the crack, allowed the crack to close, wiped off a very small amount of excess, and tied it up with 1/4" shock cord. I'll open it tomorrow and see how it looks. If I don't post again about it you'll know that the stock in now firewood and I am too embarrassed to explain what happened.
With regard to using Super Glue (great stuff when used in the right places)..be careful if you are around it too much.
Using it for model airplanes years ago, I developed a runny nose; tearing eyes and a "rough" throat. After doing some reading, I found that I was allergic to the stuff. I had to buy a fancy respirator to use it at all.
When you use it, be certain to have a fan blowing on you and be in a well-ventilated room. (I just donated that respirator to our local hospital, too).
Ever since Super Glue came out I have tried it every two or three years for the past 50 or so years. I have never gotten it to stick to anything except my fingers. Great for gluing fingers pretty much sucks for everything else. I keep thinking it may have improved so I buy some periodicly. Have two or three tubes right now. On TV it will hold a guy by his helmet to a steel beam and a tiny drop on your broken coffee mug handle and you can use it instantly. When I put it on a coffee cup handle as soon as I pick up the cup it falls off. Haven't tried gluing a helmet to a steel beam to see if it will keep me from plummeting to the ground. There is another thread going on right now about STP. Same story. The advertising is great, the product not so much.
When I used it to build model airplanes 40 years ago the brand name was Hot Stuff. It comes in different consistency, thin and thick. The thin is used to bond two porous surfaces together and uses capillary action to form the bond. Thick is for joining nonporous material. Both thick and thin work very well when used properly.