Hi sirius
sure, it is possible to do a liveabord, destination wrecks in the northern Red Sea also in December/January.
This safaries are offered all year long. Specially in this "winter" the current water temperatures are still good (around 25 C instead of usually 22 C)
The itineraries include the most famous spots, but depending on the wind there might be changes necessary.
Nearly all of the big liveaboard operators offer Nitrox on their vessels, some for free, some charge small fees for it.
As far as I know, on most of the liveaboards there are no decompression dives permitted. But deco dives are even needless, because all the wrecks (except one) are lying in a max. depth around 30m, and with Nitrox your extended bottom time will be long enough to discover them well.
If you're interested you can find more information about the Red Sea also in our dive guide
Diving Red Sea
and a list of liveaboard operators here:
Liveaboard Red Sea, Egypt
geli