A wand does not appear to be necessary for Apparation/Disapparation. The three Ds of Apparation are: Destination, Determination, and Deliberation. The actual physical act of Apparation comes during Deliberation, but is contingent upon appropriate Determination:
‘Focus your determination to occupy the visualised space! Let your yearning to enter it
flood from your mind to every particle of your body!’
Half-Blood Prince - Page 360 - British Hardcover
I kind of relate Apparation as closer to Transfiguration than spell casting. It seems, for example, becoming an Animagus would require the same characteristics: form, determination, and destination (actually taking shape of the animal form.) Similarly, Apparation/Disapparation involves the transformation of one's body from one place to another. I'm not saying it's a perfect analogy, but I liken Apparation more to Transfiguration in theory than I do to, say, Charms (which requires a wand).
Dumbledore chose not to Disapparate from the Astronomy Tower the night he was killed. He and Snape had a plan worked out that Dumbledore was determined to follow through with. It wasn't that Dumbledore couldn't have Apparated away in HBP the movie, it's that he chose not to, instead facing his final moments of life. It's really not Dumbledore's style to run from anything.
ETA: I should clarify. JKR has some input into the movies, but it is limited mainly to production and script approval. Her characters are owned by Warner Brothers, and the screenwriter (Steve Kloves is the main one, I believe) has a lot of discretion in shaping the scripts. That said, JKR had consulted with Steve Kloves regarding which parts/plots cannot be altered, as they were integral to the over-arcing plot.
Here is one movie!canon discrepancy for you though: In HBP Professor Slughorn asked Hermione what her parents do for a living, and Hermione explains dentistry to Slughorn as if Slughorn doesn't know what a dentist is; however, in the movie Chamber of Secrets, one of the points on the Weasley's big family clock says "Dentist." ;)