If you have a good fitting glue joint, you won't see any real glue line.
not much of one, anyway, and I never see it as being "white".... in fact, it's dark! And, of course, the stock should be stained with Aqua Fortis...
Use Titebond II or III glue. Fit your pieces well, glue 'em up and clamp 'em. The spring clip Pony clamps are quite useful here (not that I ever need them....) When it's dry, shape it down and re-inlet the barrel. For smaller slivers, you can actually use the barrel for the clamp.
If your repair is too visible to you and it bugs you, well, then that means it's time to practice your "aging" techniques!!! Places like that can be easily hidden.