I've never applied it to a part being turned, but I REGULARLY use CA to harden ALL my balsa nosecones and transitions.
I recommend the ultra-thin pink bottle stuff from Hobby Lobby... it's cheap and works great.
I apply it by holding the cone by the shoulder tip down, and slowly applying it with a rubbing motion using the tip of the bottle's applicator to spread the water-thin CA across the exposed (not shoulder) surfaces of the cone. The balsa wood "drinks it right in" and I keep applying it til it starts to run across the surface to the tip. It can quickly follow the wood grain channels up and start sticking your fingers, so be careful. This tells me that it's not only just "on the surface" (which thicker CA's would probably tend to be) but that it's actually penetrating the wood fiber and grain. Gloves and wax paper to set the cones on when done is probably a good idea (though I typically just use bare hands and keep my fingers moving, slowly rotating the cone, so the glue doesn't have time to stick my fingers to the cones). Transitions require a little more care to keep it off the upper shoulder area, usually apply it in a horizontal position.
I let the part "drink in" as much CA as it can handle... you'll know when it won't take any more... the stuff just 'runs off'. At that point shake off the excess and set the cone upright on wax paper to cure... be sure to do this outside with a crosswind to carry the fumes away, as CA can be rather irritating with the fumes. The cone should be completely cured in an hour or two under warm, humid conditions and ready for sanding. The CA tends to raise the 'hairs' and sanding dust inevitably trapped in/on even the most meticulously cleaned balsa surface (probably dust trapped in the pores of the grain) and "raises" it into a somewhat rough "crust" which is easily sanded down smooth with a little effort and 220 grit sandpaper.
I then use CWF thinned to the consistency of mustard brushed on with a 1 inch paintbrush and allowed to dry an hour or two, and then sanded down with 220 grit, then usually a few coats of primer, and another sanding with 220 grit followed by sanding with 440 grit paper.
Makes a balsa cone look/feel just like plastic... smooth as a baby's butt...
It won't make the cone "bulletproof" but it DOES give it considerable strength and reduces the dings and dents which soft balsa cones are prone to...
Check any of my Zooch build threads and you can see the results... Works like a champ!
Later! OL JR
PS. I've read a bit about the wood hardener stuff-- but never tried it. Some folks have pretty good luck with it, but it takes FOREVER to cure... some folks reporting that it takes MONTHS to fully cure...