If you don't have the bow tillered I would put a short temporary wrap about a inch long just over the end of the splinter, scrape up to your wrap . You will have a slightly stiff spot in your limb at the point of the crack. When you finish tillering the bow and shooting it in, remove the temporary wrap, give the area a few scrapes to blend the area to be about the same as the rest of the limb, don't flex the bow until you have the permanent wrap in place.
Of course the easiest fix would be to cut the bad limb off and splice a new limb on in the handle.
The above is a save on what would be a trashed bow. I have done some saves on bows that you wouldn't think had a chance, like this one, house fire, building structure fallen on bow breaking it from the bamboo back, through the limb and out the belly. Not too pretty but it shoots good after a dose of Urac and a bunch of sinew. You can fix seemingly impossible things with Urac, amazing stuff.
