Itamar Tas (26), a media studies student from Israel, has been asked to give a DNA sample since arriving in Queenstown on April 11 to match against anything searchers might find - from a drink bottle to a body.
However, speaking to the Otago Daily Times yesterday, Mr Tas said he would continue to stay positive ''until I see evidence she's not alive''.
''I believe she's alive. For now I'm denying any other possibility.''
He has spent a fruitless and frustrating week holed up in a Queenstown hotel room, waiting and hoping for news, as searchers continue to scour the rugged wilderness between Glenorchy and the Divide.
He spends the evenings relaying daily disappointments to his worried parents back in Israel.
Ms Okin (35) was last seen at Mackenzie Hut on the morning of March 26, shortly before she planned to tackle a challenging alpine section of the track leading to the Routeburn Falls Hut, just hours from the track's Glenorchy end.
She never made it, vanishing seemingly without trace 20 days ago, and an exhaustive air and ground search operation, launched on April 7, has so far failed to find any sign of her.
However, Mr Tas said yesterday he believed his sister was either lost after making a wrong turn or lying injured somewhere after taking a fall.
She had two years' experience serving in the Israeli Army as a communications officer in a base inside the Gaza Strip and was equipped with survival skills and plenty of food for the trek, he said.
She could be rationing her supplies while waiting for rescue, and searchers checking known accident black spots along the track had found nothing _ which ''gave us hope'', he said.
''Of course, it's difficult every day that passes, but still we hold on to hope,'' he said. ''It's very frustrating and I feel very helpless.''
It was unlikely she had made it off the track safely and simply travelled to another part of the country, he believed. She had left her passport and travellers' cheques at a house in Queenstown, and was normally in regular contact with her parents in Israel.
Mr Tas has been joined in Queenstown by friend Joe Kariv (26), who flew in from London, and cousin Ofer Avidar (39), from Australia, plus two Christchurch-based rabbis, Mendel Goldstein and Oren Raz, of the New York-based Chabad-Lubavitch outreach group of Hasidic Judaism.
''We wait every day and at the end of every day we are getting a briefing from the police about everything. Usually, there's not much, unfortunately,'' he said.
Despite the frustrations, those searching the rugged countryside were ''doing a great job'', with Sergeant Steve Hutt, of Queenstown police, in daily contact with him and his parents in Israel, Mr Tas said.
''He gives us the best feeling we could have in this position,'' Mr Tas said.
Mr Tas also accepted it was unwise to join the searchers on the track or in the surrounding terrain, as he would have liked. He had flown over the area in a helicopter and was surprised by its ruggedness.
''There's no place for amateurs out there - it's only for professionals,'' he said. ''It's very tough country.''
