Description from the sheet music at Baylor University:

WHISTLING RUFUS
"A Characteristic March Which Can Be Used Effectively as a Two-Step, Polka or Cake-Walk"
Words by W. Murdoch Lind; music by Kerry Mills
New York: F. A. Mills, ©1899.

Lyrics are identical to the second set posted by John in Brisbane above.

The following have sheet-music images of the tune only, without words:
Indiana University
Johns Hopkins University (Levy Collection)
Mississippi State University
University of Maine
University of Mississippi
National Library of Australia
York University