Yahoo! Shopping > Music has sound samples of 2 recordings, one by the Washboard Rhythm Kings from 1931 and another Dixieland version by the Bourbon Street Stompers. Unfortunately, neither sample contains any words.

The WRK version (which definitely sounds like the more interesting of the two) starts out with a little scat singing, leading me to suspect that some words may come up later in the recording. Here's the track listing for the album, "Washboard Rhythm Kings, Vol. 1"

1. Please Don't Talk About Me When I'm Gone
2. Minnie the Moocher
3. One More Time
4. Walkin' My Baby Back Home
5. A Porter's Love Song to a Chambermaid
6. Every Man for Himself
7. Please Tell Me
8. You Rascal You
9. Crooked World Blues
10. Call of the Freaks
11. I'm Crazy 'Bout My Baby
12. Because I'm Yours Sincerely
13. Star Dust
14. You Can't Stop Me from Loving You
15. Boola Boo
16. Who Stole the Lock
17. Blues in My Heart
18. Just One More Chance
19. Many Happy Returns of the Day
20. Shoot ' Em
21. Wake 'Em Up
22. Georgia on My Mind
23. Pepper Steak
24. If You Don't Love Me

There's another album by Kay Starr, called "Superb Starr", listed at Barnes&Noble, which contains the song. I transcribed these words from a sound sample there:

... but I still wish you luck with a heart that's sincere.
I won't bring any presents to you.
I ... [There were a few more words, unintelligible to me.]

Unfortunately, searching for those words with Google still didn't bring up any results.