As my research on Lena Turbyfill deepens, I have the following to offer:

apparently Lena performed a sort of vaudeville act for the local elementary school in Elk Park, North Carolina a couple of times...

all the lyrics her niece remembers are:

"I am an old man, with a stick in my hand
I go from place to place.
I'm not very good, but I try to be..."

audio: https://derekpiotr.files.wordpress.com/2022/05/i-am-an-old-man..._.mp3

some of these may be mis-remembered. any leads, anyone?
Lena would also perform "Ev'rybody Calls Me Honey" during these "variety" acts, if that places this mystery song in any sort of context.