The CA works fine, if you are worried about the Glue running about, before you glue take a Q-tip with a bit of paste wax, Johnsons works well, and rub it on both sides of the crack, Splinter, whatever you have, Not on the Crack. Apply the glue, you can buy very fine nozzles (Stew-Mac Guitar.Com, I think it is) that will fit the glue container and can be crimped even sampler. I used then followed by Medium, the thin Wicks the Medium in well. Clamp it, or push it together, spray some Accelerator on another Q-tip and wipe it on the crack. Then wipe the spot with a Paper towel, the wax can be polished of after that, sanded and the color/finish should take.
Tim C.