Disney swing!
Oh yes, I have noticed

In fact, I just DJed my local lindy jam for the first time and the Disney song was a big hit! I'd like to see if I can play one every time. Here are a few that I have in mind. Please let me know if you know of digital download sources for the rarer songs at the bottom!
Covers:
Dave Brubeck- When You Wish Upon a Star (from Dave Digs Disney)
Louis Armstrong - basically all of his album Disney Songs the Satchmo Way
Larry Clinton & His Orchestra - Whistle While You Work
Harry Connick, Jr. - A Spoonful of Sugar
Duke Ellington and His Orchestra - Sister Suffragette
Disney Originals (from iTunesd or Amazon MP3):
Lady and the Tramp: He's a Tramp
The Jungle Book: Bear Necessities, I Wan'na Be Like You
Toy Story: You've Got a Friend in Me (several great versions of this!)
Hard to find: Let me know if you have any ideas for downloading these online. I've found the CDs for sale on Amazon, but that can be expensive.
Dumbo: When I See an Elephant Fly
The Aristocats: Thomas O'Malley Cat, Ev'rybody Wants to Be a Cat
Song of the South: I have no idea what sort of treasure trove of music might be on a soundtrack of this movie, but I bet it's swingin!