I've read many threads where people who have arrived late in the day have been given a handicapped room, when they didn't need or want it. It would seem there are usually HA rooms available. Booking early may help, though it would seem that at OKW particularly, arriving early on the first day of your stay works better. But I'm sure that when making your booking, if you put it down as your first request, and you make it quite clear that it is absolutely essential, they will definitely honour it, and you won't have any problems.
I would be amazed if they didn't - but as Gilld says check with your guide to be certain.