Summer and early autumn are good times for sharks in Red Sea. But you really have to do it from liveaboard. In Sharm you may get lucky and see a reef shark or a manta on a local dive. There are also hammerheads in Straits of Tiran but you have to be in the water just after sunrise so really only double from liveaboard.
I am doing a shark intinery on Emperor Aasma a in July: Brother Islands for oceanic white tip, Deadalus for hammerheads and Elphinstone for oceanic white tip. There will be lots of time spend hunging at 30m in the blue hoping the sharks.
In October of 2018 I spent a day at Brothers and oceanic where everywhere, some of them quite aggressive. Two weeks after my visit islands were closed for diving, a few fortunately not fatal attacks on divers.
Hope it helps.
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