In May 2000 it was reported on fan sites that Aerosmith had “given” a re-recorded version of Back in the Saddle to be used in Shanghai Noon, and the soundtrack label even announced that the CD would include only Randy Edelman’s score (i.e. not the new Aerosmith track).
The film premiered in the U.S. on May 26, 2000, so if this version was used in the movie it must have been completed before then.
Given that, the re-cut likely took place sometime earlier in 2000 (or possibly late 1999). The version, credited to The Boneyard Boys (Steven Tyler, Joe Perry & Marti Frederiksen), appears during the film’s final sequences and plays over the end credits with bloopers — yet it was never released on the official soundtrack, leaving it a ghost track in the film mix.
The Back-Burner: Aerosmith Outtakes & Demos 