The Castle Walk was produced by James Reese Europe and Ford Dabney, for use by Vernon and Irene Castle. Youtube user Ragtime Dorian Henry provides the following recording:
Mr. Henry also has a website dedicated to ragtime music. It can be viewed here.
The sheet music has been made available by the NYPL Digital Collections:
The Library attributes the music thusly:
Music Division, The New York Public Library. “The Castle walk : trot and one step” The New York Public Library Digital Collections. 1914. http://digitalcollections.nypl.org/items/793719fe-64dc-8b00-e040-e00a18066fd5
Fascinating Rhythms 