I can confirm that one shouldn't trust all-purpose glue. Bought a tube of it a year ago, and out of about 10 times I've tried to use it, I don't remember a single one not needing re-gluing with something else later. All except your fingers of course - glue them, and they're sticky for weeks.
Cyanoacrylate (super glue) works best on fingers. So well in fact that it can be used as an alternative to stitches. Medical grade cyanoacrylate is a bit different (less irritant) but in an emergency, the regular household kind can be used.
I also love cyanoacrylate because it stops sticking when you apply water to it. I don't worry about my fingers, because whenever I work with this family of glues, I just keep a glass of water on my workbench, into which I dip the fingers if I notice I spilled some glue on them. The glue immediately polymerizes, and you can pull/scratch it off.