For the hell of it, I tried dubai windsurfing in google and here is one result
http://www.dubaicity.com/what_to_do_...ai-sailing.htm - 30k -
Since the coast line is now a building site almost to Abu Dhabi, you may want to consider contacting these beach hotels and seeing if they would let you store kit there.
You may have to join some sort of Hotel "Club" or simply buy a load of beer and burgers on Friday after sailing !
Looks likely you will be obliged to take some kit with you.
Good luck.