Was "Unzie" the creation of an albino gentleman already living in the U.S. or Europe?  I here propose several men who may or may not have become "Unzie".
  LOUIS WISER came from a family of thirteen kids four of whom were albinos.  It is believed Louis and his sister Annie, also an albino, exhibited together.  In 1891 Annie married Rob Roy "the Albino Dislocationist".   In order to continue in the business as a solo act Louis needed to recreate himself in a big way as albinos were becoming less and less popular on the exhibition circuit.  He already had the long hair so all he had to do was tease it the same way the "Circassian Ladies" did. Unzie appeared on the scene in 1890, the year before Annie Wiser married. Coincidence?
Like Louis Wiser mentioned above, WILLIAM CAVALIER exhibited with his sister LIZZIE as "the only twin white moors on exhibiton".  One day his sister, out of the blue and without telling William, decided to marry the museum lecturer. William was furious and in failing to stop the wedding from going forward swore vengeance on his brother-in-law.  The wedding took place in 1889.  Unzie appeared on the scene in 1890. Did William get the ultimate revenge by becoming "Unzie" and making more money as a solo act?
ARCHIE BONNEY was billed as the "Swiss Warbler and Accordionist".  Was his career going nowhere?  Was the novelty of his act wearing off? He was born in Scotland as was Rob Roy, the fella mentioned above who married Annie Wiser.  Was he Rob's brother?  He already had big teased hair all he had to do what let it grow out even more and maybe in a year he could have a new act - "Unzie, the Australian Aborigine Beauty"
KARL BREU as "Tom Jack, the Ice King" was a popular act in Europe. He later changed his name to Toya and toured with his albino "Ice Family" and even came to the U.S.  Was Unzie a member of this family?  Are his origins in Europe? Did the family come to the U.S. and one of its members decided not to return to the Continent?
One other theory exists. 
   In a small news article Unzie is quoted as saying, "My eyes are not exactly those of the albino, but a very delicate blue."
   Was Unzie even an albino?  Did he let his hair grow long, tease it and bleach it?  Did he simply bleach his mustache and eyebrows to complete the look?  In his photos you'll notice he has no eye problems.  Many people with albinism are legally blind or they have a wandering eye or one of the eyes shakes back and forth.  Most were sensitive to light and for that reason kept their eyes half closed.  But Unzie's eyes look quite normal.* Was he a self-made freak like the tattooed man or Circassian lady?

*However one small article did mention "his lovely pink oscillating eyes."