My grandfather used to sing it to my Mom and her siblings when they were children. It used to freak her out because he sang it with a different ending where the dolls were destroyed. Sorry, I don't have the lines to that one. Her father always recited kind of morbid poems and songs to them. In his version it was a "cucumbie boat" rather than cucumber.

I found one other person on the internet who had referenced this song but the link is now gone.

My grandfather was born in 1899.

He also used to recite Little Orphant Annie and "Down Went McGinty to the Bottom of the Sea, dressed in his best suit of clothes, clothes, clothes."

My email is: kwalstedt@gmail.com if anyone wants to chat.