Che was reportedly clean shaven when he lived in Argentina. The Che in the Prince production was clearly modeled on the Cuban revolutionary Che, down to the beret and the olive fatigues (and, I guess you could argue, even the cigar he's puffing on his entrance). Prince went with this historically incorrect image, one suspects, for a very specific reason.
TT
"Me flunk English? That's unpossible!" - Ralph Wiggum