Unfortunately, general aviation in Dubai is virtually non existent, everywhere :
I unfortunately do not know about Abu Dhabi, but in Dubai, I think there is a cherokee for rent at Dubai international, but i'm sure its expensive and I would guess you will spend the better part of 30 minutes waiting to take off. Everything else is too far. Maybe somebody has more specific info on Abu Dhabi, but I hate to say it, I don't think there is anything up that way. Sorry.