According to "Klezmer! Jewish Music from Old World to Our World"
by Henry Sapoznik, this song was popular with klezmer bands in the 1930s and the final word of the title was written "shayne" when transliterated to English. When the Andrew Sisters recorded it, the last word was written as "schoen" mit an umlaut over the "o" so it would appear to be from German instead of yiddish in order to sell more records in those antisemitic times.
If the Andrew sisters had recorded the song a few years later, anti-German sentiment might have been stronger than anti-Jewish sentiment.
Bev and Jerry