I found the author of the text that Cetmst posted above. It's John W. Ivimey, born 1868. The Library of Congress has 5 different editions, made by 4 different illustrators. The title also varies:

Complete Version of ye Three Blind Mice ... illustrated by Walton Corbould. 1904

Complete Story of the Three Blind Mice ... illustrated by Paul Galdone. 1987

Complete Story of the Three Blind Mice ... illustrated by Victoria Chess. 1990

Three Blind Mice: The Classic Nursery Rhyme ... illustrated by Lorinda Bryan Cauley. 1991

Three Blind Mice: The Whole Story ... illustrated by Walton Corbould. 1995

Complete images of the original Corbould version can be seen at the Internet Archive (PDF).

Jonathan Edwards recorded it on his album "Little Hands" in 1987. You can hear it on Spotify or YouTube.