I suspect the song Skip desperately wanted is this one. (Do you suppose he's still desperate?) It's sometimes classified as Cajun, rock, rockabilly, or country. Dan Newton and the Shoe Band performed it on A Prairie Home Companion, July 6, 2002. The link will bring you to a page where you can play the audio file.

MATHILDA
George Khoury and Huey Thierry, © Combine Music Corp. (BMI)

CHORUS: Mathilda, I cried and cried for you.
It makes no diff'rence what you do.
Mathilda, I cried and cried in vain.
I want my baby back again.

1. You gave me love when there was none.
You know that you're the only one.
Deep in my heart you will remain.
I'll always love you just the same. CHORUS

2. My love for you will always be
Such a precious memory.
I'll always love you, come what may,
No matter what you do or say. CHORUS

[Recorded by Van Broussard, Cookie & the Cupcakes, The Fabulous Thunderbirds, Freddy Fender, Clarence "Frogman" Henry, Sleepy LaBeef, Jerry Lee Lewis, The String-A-Longs, The Texas Tornados, and several others.]