I tend to use "a cappella" instead of "unaccompanied" because the latter might simply mean "alone", "with no one else". It's not strictly vocal, as witness the Bach suites for unaccompanied violin. Nor does it necessarily preclude a performer from accompanying himself. I also don't like defining things in terms of what they are not. Why should there be an automatic presumption of accompaniment, particularly with trad folk songs??