Related songs posted in other places:

In the DT: Old Shoes and Leggin's.

In the DT: Grey Beard Newly Shaven

Old Shoes and Leggings in the thread "Songs your parents didn't allow"

With His Owd Grey Beard New Shaven in the thread called "Songbook - Folk Songs Of Lancashire"

Several versions in the threads called Crazy Old Man from China and A Children's song from the 70s