If I understand correctly what you are saying is tht the white King is forced to move otherwise it will be captured on the next move ... but what if the move is not necessarily to the edge ... I think a draw is still valid here ... and what if white can show that any other move will eventually lead to a forced capture be it in two, three, four or more moves?
(kaŝi) Se vi volas saluti iun en ties denaska lingvo, provu nian 'vortaron de ludanto', en la ligo "pli pri lingvoj" sub la flagoj. (pauloaguia) (Montri ĉiujn konsilojn)