When the new super bonding glues first came out, they were hailed as the best thing since sliced bread. Until someone got their hand stuck to the breadbox.
Super Glue is indeed great stuff, and certainly can create a secure bond. But when that bond is between your fingers and something else, or the glue is a puddle on your kitchen counter, a wet paper towel is not going to get you very far, because it will be stuck to it, too.
If you're going to have a tube of Crazy Glue in the house, the smartest thing you can ever do is to buy the solvent at the same time. It's just the nature of Man, that sooner or later someone will have even a small accident that is only a drip or spot, but which could turn into a major problem if they can not get it cleaned up.
If you do not have the solvent, or do not know where to find it, here are a few tips you can try. Many emergency hotlines will recommend using vegetable oil for skin-to-skin bonding of fingers. This has mixed success.
Because the active ingredient in Crazy Glue and other super bonders is cyanoacrylics, what you really need is 100% acetone. While some fingernail polish does contain this, it's not usually in the strength needed to break the bond. However, for something like a spill or drops on a surface like a countertop, if you pour the nail polish on and let it sit for 15-30 minutes, it may do the trick. Otherwise, you should try a hardware store for the acetone.
Some users report successful removal with lighter fluid. Keep in mind though, that anything of a chemical nature can damage the item with the glue on it. Test a hidden or small area of material or surfaces with the glue on it, and wash hands immediately after having it removed from your skin.