While it doesn't fit the "unobtrusive" part of the requirement, a saxophone takes less breath than a recorder and the fingering is not that different.

Clarinet takes even less wind but the fingering is a lot more subtle.

Think again about the fiddle. It isn't really any harder to place your fingers accurately on a fretless instrument than it is to blow a recorder accurately enough to be in tune. The bowing is the hard bit, not the left hand.