Will this run be exposed to the weather or will it be under a roof so the floor stays dry?
Straw in a hen house attracts red mite and personally I would not use it at all. It might be ok in a covered run though.
Sand is probably the better option for covering slabs with, but is there any reason why you can't remove the slabs, dig out the run to a depth of 4 - 6 inches and backfill with wood chip? This would give the hens the option to dig themselves a nice deep dusting crater.
Hens won't worry about the sand being cool, they will probably prefer it.