Is it textured ? Sometimes hard cycs have a very tiny "popcorn" finish to them if that is the case I'd say vacuuming is going to be the only answer. If it's perfectly smooth you could try a very dilute mixture of TSP and a sponge mop and then hours of rinsing. If possible, perhaps blowing it off with compressed air, whilst running a particulate air cleaner, then painting over the surface with a new coat of paint.
I'd guess repainting might be easier and more effective than cleaning. In the TV world, cycs are painted slightly grey-white, as pure white pops too much on camera. I wanna say it's like 18% grey, but don't quote me. For theatre, it probably doesn't matter that much.