Yes, you should print out the hand-outs. I would not expect many people to remember all words, esp. verses, even if they remember the choruses. But even those who remember all words will appreciate the handouts, as I would do.
When talking about 1940s, you cannot forget the domination of Glenn Miller Orchestra at all charts of the period. GMO dominated peoples minds so much that their style, first classical swing, like in Tuxedo Junction (that I linked below), then jive, like In The Mood posted somewhere above) were essentially copied by most musicians of the time. Remember, GMO in 1940s was like Beatles in 1960s-70s. Of course you cannot teach to sing In The Mood or Tuxedo Jnct, because Glenn didn't want any words there, but everyone should remember the jivey sound of In The Mood, the no1 in popular music of 1940s, eventually taken further into
Bebop style by jazz musicians like Charlie Parker.
If I may introduce my opinion here: this type of popular music (created long before I was born) was far more interesting than today's pop. E.g. listen to the Blueberry Hill, or Autumn Leaves (the all times jazz classic of that period - I hope you include it in your list because knows it) just follow the baseline and your ear enjoys multitude of interesting chords. You hear every possible chord from from the G-minor scale the song was written in. While today's pop are at most repetitive I-IV-V (sometimes I-V only) progressions. It feels like in popular music (not in classical & jazz, that's a different story) people have forgotten the richness of musical emotions their fathers used to express. That's my "technical" way to explain why old music is perceived as "better" or "more interesting" by some, including myself.
Anyway, enjoy your work assignment, I'm sure you'll like your role & do well in it.