The best and safest way to clean a stylus effectively.
Get a 1/8" wide artist brush and with a very sharp scissor cut the bristles halfway down and across at a right angle. This stiffens the bristles a bit. You can use it dry to knock of dust or wet to clean off residue. I use a little spray bottle of eyeglass cleaning solution. You do not want the brush too wet, just damp is fine. With an artist brush you can safely brush the stylus in any direction.
Blue Tack is dangerous and ineffective. It will remove dust but not residue. One false move and you snap your cantilever off.
Lyra Stylus cleaner is awful especially when you consider the price. The eyeglass cleaner is way better and cheap to boot. It removes deposits quickly with just a few brush strokes. The Lyra frequently did not work at all. Alcohol will not effect the cement used to fix the stylus. Prolonged exposure to acetone would and perhap lacquer thinner. I once took an old broken cartridge and tossed it in brake cleaning fluid overnight and the stylus was still well cemented in the morning. I have also done this with records with no noticeable ill effect.
I clean the stylus about once a week. I use a conductive sweep arm during play and the dust cover is always closed. I hardly ever have dust on the stylus, but a small amount of residue will collect above the contact patches. It does not affect play until it is severe enough to see with the naked eye.
