Originally posted by Ushgarak
Whilst it is indeed in the EU that the sabre was constructed that way, it was also in the ROTJ radio play, which has always given it a slighty more respectable status.
The scene was definitely scripted and storyboarded for the movie although never included in the published shooting script - Vintage 77 has posted some of the storyboards in the OT Pictures thread.
No pictorial evidence has yet surfaced to show the scene was ever actually filmed (and I doubt it was).
Curiously, John Williams seems to have scored music for this scene though - much of the music from Tatooine Rendezvous, from the Special Edition soundtrack, is thought to contain cues from this scene not included in the movie. The liner notes to the CD also suggest that Vader tries to contact Luke through the Force during this omitted scene.
As for the Tydirium - that was just one of many Lambda Class Shuttles used by the Empire, although it was at one point used as a personal shuttle by Vader himself.
Vader is using a different Lambda Class shuttle by the time of ROTJ, I'm not sure of the name.
The EU tells how Wedge Antilies and Ace Azzameen stole the Tydirium from the Empire prior to the mission to Endor