Your timing of mid-November to start of December is perfect for doing a liveaboard in the Red Sea and the best time of year for getting to see sharks...it is also my favourite time of year to do a liveaboard in the Red Sea!
There will be oceanic whitetips (longimanus) at both Brother Islands, Daedalus Reef, Elphinstone Reef and Rocky Island.
There will be thresher sharks at Brother Islands and possibly also Daedalus Reef.
At Daedalus Reef you will have schooling hammerhead sharks.
And if you are lucky you can also have silky shark at Daedalus Reef, Elphinstone Reef or Rocky Island.
And if you are really lucky maybe even tiger shark or whaleshark...
Of course there will be some grey reef shark around...but who cares about them when there is oceanic whitetip and schooling hammerhead sharks around! ;-)
Water temperature will be 26 degrees Celsius...though perhaps with the odd one or two 3-4 degrees colder thermoclines.
The weather will be around 28 degrees Celsius in the daytime and as it is the Red Sea it will be blue skies and no rain.
Also usually the wind is still quite calm in November-December, so calm seas for the sailing and to dive in.
There are a few liveaboards that sometimes do 14 day trips - great value and you also get more 2-3 more diving days for your money as you spend less days in port as when compared to doing a back-to-back liveaboard (2x7 days).
If you cannot find a 14 day trip that fits with your travel dates I would recommend doing these 2 classic 7 day trips:
A) Daedalus Reef - Rocky Island - Zabargad Island - St John's (often also includes Elphinstone Reef)
B) Brother Islands - Daedalus Reef - Elphinstone Reef (BDE)
I have done more than 20 liveaboards in the Red Sea. My favourite boat is the SevenSeas...but unfortunately she is also popular with other divers and therefore is often booked out.
Virtuelle Tour
But don't worry too much....there are many liveaboards boats to choose between in the Red Sea and they are all really good