I'm somewhat new to working in an office environment so the subtleties of what constitutes public and private behavior may elude me. That said, I have a coworker who once a week straddles his trash container and cuts his nails. I can't stand the sound of this and warily watch for the errant clipping heading my way. I'm dumbfounded on what I could possibly say? I suppose we are all lucky he doesn't clip his toenails. Help!
Etiquetteer's first reaction on reading your query was a piercing "Eeyew!" This sort of public grooming needs to stop. Etiquetteer firmly believes that no one should have to "see the magic happen," or hear it, either.
No one should leave home without being fully dressed and fully groomed.* A nail kit of pair or nail clippers for emergencies should be kept at the office, but taken into the restroom to be used.
Most problems like this don't get resolved without actually having a conversation with the offender. Someone will have to Say Something. The goal, of course, is to stop the behavior, not to shame the offender. As a newcomer, it might be thorny for you to do so; you don't want to get a reputation as a complainer so early in your tenure. Your colleague's supervisor should be informed, discreetly, and asked to address this issue with your Clipping Colleague. An office memo reinforcing Perfectly Proper behavior might work depending on the size of your workplace. You could even send a gift card for a manicure with the heading "It's time to put the man in manicure!" (While it's dangerous to assume, Etiquetteer believes this must be a man.)
If those options aren't open to you, and you don't find it possible to step out for a coffee when your Clipping Colleague is clipping, then take a deep breath and have a quick private conversation. Apologize for raising the issue, be honest about the impact of his behavior, and ask if he could take his clippers into the restroom. Etiquetteer hopes your Clipping Colleague will take this in the spirit intended.
Best wishes for a successful outcome!
*Yes ladies, that means not applying your makeup while behind the wheel or on public transportation.