You will have to try this out! Capacitive sensing is sensitive - very sensitive, sometimes too sensitive, but also works with quite small signals.
Distance through air: well, look at a Theremin how far it can detect hands in air.
I have a sensor here that can sense water through the wall of a non-conductive pipe (5 mm is no problem).
For you: most sensible would be two copper traces next to each other, with some non-conductive paint to cover them, and the metal object to be placed in between them. Should be quite easy and reliable to detect. Buy a few of those cheap water sensors with lots of parallel traces and start cutting away, that may be the easiest/cheapest way of building such a configuration (try it out with pieces of film first).