I'd use super glue! There are generally three viscosities of super glue available, thin, medium and thick. (Hobby Lobby has all three.) For this I'd use the thin, it is as thin as water, so be very careful using it because I have glued my fingers together with it many times. Find a big sewing needle with an eye that will hold about 1 drop of glue, put one drop of glue in the eye while NOT holding the needle over the wood, then touch the eye to the wood to transfer the glue. You might try practicing a few glue drop trials on a wood scrap before proceeding on your stock! Don't try to apply the glue from the spout directly to the wood, you'll get way too much and it will run down the wood causing a big mess. The glue is so thin that it runs into the finest cracks (I've applied it to a small knot on one side of a butt stock and had it run out on the other side), with no need to lift the splinter with small needles to get the glue under there. In small drops it dries in a minute or two, and if desired, the splinter can be held down into place with the eye-end of the needle. Reapply once dry to further fill any remaining void, adding sanding dust if desired. Sand and stain/spot refinish as needed. Good luck, sir!