I don't do anything special to protect my hands. Just wash them when I'm done, scrub the fingernails with an old toothbrush if they are super dirty and make sure I lotion them up or put Vitamin E or Cuticle Oil on my nails every week or so just on general principles. I think I get more hand/nail damage from household cleaning than I do from cleaning guns.
Either that or you can go to any medical supply store or pharmacy and pick up some size specific latex gloves that are a little thicker but nicely form fitting so you aren't feeling like your wearing oven mittens while cleaning.
Truth be told, I've been known to steal a pair or two of small size latex gloves whenever I go to the doctor's office...lol. They are just that much thicker and nicer than the crap you get at box stores like Walmart.