Good god, just put no criminal record on the application and see what happens. If they check and find it and you don't get the job, you won't be any further behind than if you put you have a DUI and they reject you. Of course if you have to provide a clean criminal record check that could be difficult. You say it's on record in a certain state, perhaps you could have a check run in another state that wouldn't show it? There are always ways.
As far as lying on the application, after living there for a decade and being basically lied to constantly I'd have no problem whatsoever for something like this. Bite you in the ass? There are so many other things that could do that to you on a daily basis in the ME it doesn't bear worrying about. As long as you don't talk about it once hired.
If every criminal was ejected from Dubai the place would be empty.