There is no possible way Japan would be remotely interested in or in a position obtain Alaska from Russia until the early 20th century, presumably as a result of a settlement in an ATL Russo-Japanese War. If such an outcome appeared remotely possible to the USA or Britain, either one would step in first and either buy Alaska themselves or just take it in the aftermath of a Russian defeat. By 1905, the US, in particular was far too concerned about the "Yellow Peril" to allow Japan any holdings in North America.
Of course as others have said, a world in which Russia never sold Alaska to the US in the 1860's might be so different from OTL as to make reasonable speculation about this difficult.
Well america buying alaska was kinda unexpected too. Plus the idea of a japan boost sounds like a good TL.