Harmonicas are not designed to be played one-handed, though they can produce a tune that way, or in a neck rack; the resulting quality can range from pretty good (Andy Irvine accompanying his songs) to terrible (B*b whatsisname) with the emphasis on the not-very-good end.   Harmonica playing in which the harmonica is the real point of the thing ideally requires both hands, which are used to form a cup around the harp that plays a major part in forming the tone produced. So not a true one-handed instrument.