DH and I had a 1940s wedding complete with a big band. (This was 1998). So I had done some research and maybe I can help.
There was a CD collection by Time/Life that went through the best of each year of the 40s. So "1941" would be the name of one CD, and the jukebox is on the cover; that's how you can tell it's the right one. You can try google to find it. Meanwhile,
Here is a link to a few on ebay and there is another little grouping currently for sale on there (and some awesome collection that just sold--darn)http://www.ebay.com/itm/YOUR-HIT-PARADE-1940S-BIG-BAND-POP-DOO-WOP-1991-TIME-LIFE-MUSIC-3-CDS/171539059581?_trksid=p2047675.c100011.m1850&_trkparms=aid%3D222007%26algo%3DSIC.MBE%26ao%3D1%26asc%3D29385%26meid%3D4f2609e30e2a4d339d4bbbbf5213506e%26pid%3D100011%26rk%3D3%26rkt%3D4%26sd%3D300939550397
Ok that being said, off the top of my head (some might not quite be 40s)
Volare (Dean Martin)
Night and Day (Sinatra)
Tangerine (Helen O'Connoll, Jimmy Dorsey)
Slow Boat to China (Kay Kyser)
Moonlight in Vermont &
Haunted Heart (both by Jo Stafford)
Tie a Yellow Ribbon (round the old oak tree)
Glen Miller Orchestra (Moonlight Sernade, String of Pearls, Chattanooga Choo-Choo, etc)
Frank Sinatra (I always liked Frank Sinatra's CD called "Duets" which were made in the '90s, but they were the old songs…or you can just go with the originals)
And here is the magic bullet…you should be able to buy DVDs of "The Lawrence Welk Show," --this, OP, many of that generation loved loved loved. Not music but comedy they tended to love was "The Carol Burnett Show."
Finally, THIS CD is great. It's a compilation of hold music for Pottery Barn that people loved so much they started selling it. Just great old songs. If it's out (I see there's only one left) just get the songs individually on iTunes.
http://www.amazon.com/Dinner-at-Eight-Pottery-Barn/dp/B000CCDQXY/ref=sr_1_1?ie=UTF8&qid=1428366770&sr=8-1&keywords=pottery+barn+CD