It doesn't exist. The show was produced by Mike Todd to run at the 1939 New York World's Fair. Then it played Broadway for a short period. It starred Bill "Bojangles" Robinson, the great African American song-and-dance man, now sadly mainly remembered as the courtly adult in Shirley Temple movies. During the 20s and 30s he was a beloved star. The show was actually only one of two musical versions of The Mikado to play that summer. Another troop of black performers did a ripoff called "The Swing Mikado" on Broadway for the WPA. Both shows ran 85 performances.
Obviously, this was before the time of original cast albums.
http://www.broadwayworld.com/board/readmessage.cfm?thread=972787#3631451
http://www.broadwayworld.com/board/readmessage.cfm?thread=963561#3533883
http://www.broadwayworld.com/board/readmessage.cfm?thread=955158#3440952
http://www.broadwayworld.com/board/readmessage.cfm?thread=954269#3427915
http://www.broadwayworld.com/board/readmessage.cfm?thread=955012#3441622
http://www.broadwayworld.com/board/readmessage.cfm?thread=954344#3428699
