This is what I do when I'm in your situation:
1. Watch the DVD once to get the feel of the piece.
2. Watch the DVD again and write down all of the choreography in short phrases, like broken sentences.
3. Time stamp each line to the best of my ability.
4. Go into rehearsal and adjust my script to match what this company is doing.
So my script will start to look like this (based on the video):
10:54 Pink Girl Ent UR, x to DL
11:15 Red Man Ent UL, barrel turn around stage,
11:25 Red Man meet Pink Girl DL
11:45 Red Man lift Pink girl CS
Depending if they use their own sets/costumes or a rental from the DVD cast, the costume colors may not be the same, and in most cases, for a man's variation, his entrance may change. Most dancers have a side they perform better on, so you might find by watching your rehearsal that now the Red Man enters from UR, and instead of a barrel turn, does a series of tours (jumping in the air while turning a completely around) to meet the Pink Girl DL. Then you may find a lot of the choreography matches the video, while other small parts change.
There are 2 main versions of that ballet, and it's helpful to know if your company will be dancing the version in the video (with small adjustments as the director warned you) or if it's someone else's interpretation of one of those. A lot of companies will base their own piece on the Petipa, so while many sections will remain the same, they may be put in a different order, or some sections may be replaced with another version's section altogether (this is very common).
It is worthwhile to watch the video and take your notes, as you don't know how much differs, and you do have the opportunity to rewind and catch things you missed. Should you get lost, you always have your time stamps to help you find out where you should be. (This is also based on idea that the rehearsal you're watching hasn't slowed down or sped up the music in relation to the video.)
The other thing I do, when no video is available, is to sit in rehearsal and write down everything as it happens, doing my best to keep my line breaks and catch time stamps. In this case, it is helpful to know everyone's name or have them in costume so that you can refer to them by costume color/character. I'll admit, doing it this way is harder, so I suggest writing your script based off the video, then updating it as you watch the rehearsal.
If a musical cue is ever needed, and a score is not provided, I find it helpful to do this:
15:45 Blue Girl Ent SL1 - Start Counting
15:58 LX 45 1-2-3, 4, 5, 6, 7, 8 2-2-3, 4, 5, 6, GO!
To me, that means that the first 3 counts are close together, while the 45678 are a bit longer. Then the phrase repeats with the 223, then the long 456, then I call GO on where 7 would be. (I've found this is the way most choreographers count as well - not in measures, but in phrases. While that above may look like 2 measures, it's most likely 6+ measures. Then you're at least counting the way the choreographer does and it's easier to communicate.) Time stamping is also helpful, though I wouldn't use it to call the cue necessarily, in case you're working with a live orchestra, or you're working with a CD that will require you to stop between tracks for applause and restart the CD when the applause begins to die down (which will throw off all of your time stamps completely).
If you want, I'd be happy to email you a copy of one of my scripts, if you want to see the layout. PM me if you're interested.
Best of luck! It's not as scary as it sounds. Just a little overwhelming when you start, but you'll get the hang of it quickly.