As a general rule, ancient coins are much more robust than their modern counterparts. They've survived being buried in the ground for nearly 2000 years, then being dug up again and subsequent washing. You don;t have to worry about leaving fingerprints behind, or accidentally disrupting the lustre - you've got to really abuse them to do any kind of lasting damage. While they're by no means indestructible - ancient bronzes are even more susceptible to outbreaks of bronze disease than a modern bronze or copper coin - it's usually quite safe for them if you hold them in your hands.
Indeed, you're more likely to suffer more from the experience than they will. Some ancient bronzes contain a surprisingly high level of lead. So wash your hands both before and after you handle your ancient coins.

Sel, it's usually sulfur in the paper that's considered detrimental to coins, rather than chlorine.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis