You should be more specific. "Unsung" just means under appreciated. An unsung hero would just be a hero who people don't appreciate enough. Could be anything, a doctor, a soldier, a fire fighter, etc. But not all of those would necessarily fit into the parameters of your story. For example, if you're writing about somebody who saves a drunk who fell on a subway rail, it wouldn't make sense if they're a soldier. It's difficult to just create a character from scratch and then hope they'll fit into any given scenario.
"No-one would really think he could be a hero" You could just have them be a regular person. A cashier at a convenience store that stops a robbery, a valet person who helps someone out of a burning car, stuff like that. People typically don't expect ordinary people to intervene in dangerous situations, so anything like that would mean that no one would think he could be a hero (Plus people dig that kind of soppy stuff). It would be easier though if you know what they're a hero for.
