Cyanoacrylate wasn't designed for porous/fibrous materials like wood. I'd use T-88 epoxy, which is.
Insert the stem to open the crack as much as "naturally" possible without making it worse (do NOT insert a wedge or otherwise try to pry the crack open). Press-wipe as much T-88 as you can into the crack, remove the stem, and gently wipe away the surface surplus with a vinegar-dampened paper towel or piece of old T-shirt. Then clamp the crack if needed with a rubber band. (If more epoxy appears, wipe it away also). Finally, check the mortise to see if any glue squeezed into it, and remove with a twist of paper towel dampened in vinegar if so.
After the epoxy is fully cured, then tune the tenon's diameter to be the lightest secure fit possible, to reduce outward pressure on the repaired crack.
Such a repair is nowhere near as bulletproof as a band, of course, so handle the pipe with TLC forevermore, also checking occasionally to see if the crack has re-appeared or lengthened. If so, stop smoking the pipe until a further course of action is decided, because it will only get worse.
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