I think there is a grain of truth to your stereotype, yet in Norway at least, hanging/choking are the most common means of suicide for both genders (although as you allude to, women do resort to poison more often than men). What is imo more interesting, is that males who try to commit suicide have higher "success rates" than women for any given means. E.g. a man who hangs himself has a higher chance of dying than a woman who hangs herself.