You can hear the complete song at The Red Hot Jazz Archive. There, Ida Cox is credited as songwriter, as well as the singer. I diligently compared that recording to the one in DigiTrad, and I found several differences, which I have marked with boldface.

WILD WOMEN DON'T HAVE THE BLUES
(Ida Cox)

I hear these women ravin' 'bout their monkey men,
About their triflin' husbands and their no-good friends.
Peaceful women sit around all day an' moan,
Wonderin' why their wanderin' papas don't come home,
But wild women don't worry. Wild women don't have no blues.

Now when you got a man, don't never be on the square,
'Cause if you do, he'll have a woman ev'rywhere.
I never was known to treat no one man right.
I keep 'em working hard both day and night,
'Cause wild women don't worry. Wild women don't have the blues.

I've got a disposition, and a way of my own.
When my man starts kicking, I let him find another home.
I get full of good liquor, walk the streets all night,
Go home and put my man out if he don't act right.
Wild women don't worry. Wild women don't have the blues.

You never get nothing by bein' an angel child.
You better change your ways, and get real wild.
I'm gonna tell you something. I wouldn't tell you a lie.
Wild women are the only kind that really get by,
'Cause wild women don't worry. Wild women don't have the blues.

[As recorded by Ida Cox accompanied by Lovie Austin and Her Blues Serenaders, 1924.]