It doesn't hurt to run some super glue into those end grain cracks found under butt plates, grip caps, ect either. The glue soaks in and runs into the cracks like penetrating oil into a steel joint.
It's amazing how far some of them run into the butt stock. I just did some up on a Model 31 stock and had the glue start to pin point dot the out side of the stock 2 inches from the end from following the flame grained AmWalnut.

I usually clamp a chip in place using superglue. The chip fits tight to begin with but a little oversize. Then the clamping forces it into the check or damaged area.
It may even crumble the tiny chip a bit, but all the better as it will be force fit of sorts and no hint of a line exists around the repair.
When sanding the repair off, as a final finishing touch, you can
leave the fine sanding dust on the surface, run some more superglue onto the area and then quickly resand it again,,, glue, sandingdust and all. It will quickly harden over but will fill any small imperfections or pores that might have been showing. Maybe you want them to show, in which case you fore go this step.
Any solvent based stain will penetrate it easily, but it should be taken down level with the original wood surface so as not to leave a glaze on the surface anyway.

The pieces used and the repairs being made are small and there's no chance of the method pushing the wood farther apart by wedging. We're only talking repairing small cracks and damage.

FWIW,,Super glue is a pretty good locktite too in an emergency,,but you have to get the screw down fully into position fast! or the stuff will set up on you and be stuck w/the fastener half in,,half out.
The restricted space must make for the instant set up.
It'll take some heat on the tip of the screw from a soldering gun to loosen it usually,,it holds quite well.
Works metal to metal, or metal to wood. (tooth repair! ouch..)
Good clean surfaces of course.