Here's the recording by Cannon's Jug Stompers. I think the Genius.com recording is just wrong, but I admit that one the first time around, it's hard to tell what they're singing. Every other time around, it's clear that they're singing "new way of talking."
https://www.youtube.com/watch?v=7uhRyg5jO6Q

Here's the Genius.com transcription, with my corrections.

WALK RIGHT IN
(Gus Cannon/Hosea Woods)

Walk right in, set right down
And baby, let your mind roll on
Hey, Walk right in, stay a little while
But daddy, you can't stay too long
Now, everybody’s talking 'bout
That [???] way of walking
Do you wanna lose your mind?
Hey, Walk right in, set right down
And daddy let your mind roll on

Walk right in, set right down
And baby, let your mind roll on
Walk right in, stay a little while
But daddy, you can't stay too long
Everybody’s talking 'bout
That new way of walking
Do you wanna lose your mind?
Walk right in, set right down
And daddy let your mind roll on

(Play it, man)

(Blow it, Cannon) - kazoo/harmonica

Walk right in, set right down
Daddy, let your mind roll on
Walk right in, stay a little while
But daddy, you can't stay too long
Now, it's everybody's talkin' 'bout
That new way you're walkin’
Do you want to lose your mind?
Walk right in, set right down
And daddy let your mind roll on