Alaska was purchased by the USA from Russia in 1867, so it was an American possession after that and no passport would be needed.
It's reasonable to think William went by boat from San Francisco or Seattle to either Juneau or Skagway in Alaska, from where he made his way over the Alaskan Panhandle to the gold fields of the Yukon (assuming that is in fact where he was going).
Since Yukon was of course part of Canada's North-West Territory in those days, the North-West Police (now called Royal Canadian Mounted Police - RCMP or Mounties) were in charge of law and order and recording any problems, including fights, injuries, or death 'by misadventure' of whatever sort.
If you really think Wm Barlow got to Alaska, or at least settled there after the Gold Rush of 1898, you could try contacting some of the 41 BARLOW names I see in Alaska's phone listings and find out what they know. There is always one person at least who is the family historian who can give you some info.
If you think something (good or bad) might have happened to him in Canada, you might try contacting the RCMP in WHitehorse, Yukon, for a few e-mails or phone/fax contacts of museums, libraries, or archives that would have some info about him.
Royal Canadian Mounted Police WHITEHORSE 'M' DIVISION HEADQUARTERS 4100 4th Avenue Whitehorse, Yukon Canada Y1A 1H5
Tel: (867) 667-5551 Fax: (867) 667-2621
or go through - www.gov.yt.ca - and ask the Govt of Yukon to direct you to the same kind of info sources.