The Sheraton Deira is actually closer to the airport than the Hyatt. So probably a better bet for you, Mark. Not far off being directly under the flight paths for one of the runways.
(When I posted yesterday, I was thinking about the other, older Sheraton, on the Creek side - which would not be suitable for you. Hence the alternate suggestion).
Loads of Sheratons, Hyatts, etc etc in town now. Make sure your taxi knows exactly which one you want.