Yes, sharks do frequent the Red Sea around Sharm el Sheikh. In fact, a whale shark was spotted a few weeks ago, unfortunately I did not see it. There literally tens of dive operators in the Sharm area and most will have an operation running from the hotel. The dive operators that I know of with predominantly English speaking staff are Ocean College, Camel Divers, Aquarius Divers but there are probably loads more.

With regard to sharks, I understand that Hammerhead sharks normally school around Jackson Reef (one of the Tiran Island reefs) during the warmer summer months (June - September).

I hope this helps, but it may be best to contact the dive operators direct for more detailed information as to what they can offer in the way of diving.

When we were there last year there were no notifications of any sharks apart from the usual hammerheads

there had been a whale shark in January and also some sand tigers
but the reef aharks were absent