A possible theory to the missing Execution scene
If you remember watching THE FOUR MUSKETEERS on TV or VHS before 1997, you probably viewed it on a crappy print with even crappier pan-and-scan (remember how the opening credit scene would constantly pan-and-scan to catch the credits appearing left and right?). This also removed Milady's execution sequence.
Interestingly, Michael Hardwick's novelization of THE FOUR MUSKETEERS omits the execution as well. It adds onto the scene of Athos stopping 'Nun' Milady at gunpoint. Athos shoots her dead.
Recently, hearing Ilya Salkind's commentary on SUPERMAN II, he talks about THE FOUR MUSKETEERS. And he provides a key to this omission. It seems Richard Lester did not intend to film the execution sequence, feeling it was too gruesome. His omission intent must have been standard enough for Hardwick to write the novelization in his vein.
Ilya claims he pressed Lester to film the execution scene (which he portrayed in long distance). They showed two prints to preview audiences, one with the execution, the other without it. Audiences were more approving to the former.
Yes, this is Ilya Salkind we are talking about, but the evidence here seems solid.
For awhile, there had been some copyright issues about releasing the two films. Could the print that appeared on VHS and television be a bootleg of the preview print that excised the Execution scene? Probably.