As far as I am aware it's no different to say walking along the routeburn or Kepler with a rifle. No bolt in,mag empty, pointed In a safe direction at all times. And then venturing off and putting the bolt in and filling you're mag 500m away and not pointing towards the track.
However having checked DOC website it shows no information regarding hunting or fishing. Best to ring the Te anau office to find clarity on the matter.
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