Osmium tetroxide production
A block of Osmium is quite immune to atmospheric attack, due to the low surface area of the osmium, but when heated it can form Osmium tetroxide. I wouldn't like to risk wearing an osmium ring just incase Osmium tetroxide is formed. The oxide has a pungent smell so if you do wear a ring of Osmium, at least you'll have some form of warning to take it off. So really, I wouldn't recommend it, but do it at your own risk.