Hay is always gonna get everywhere but I find using baled hay helps because it tends to be longer strands. I keep a bale outdoors and give the hay a quick shake and put it in a tub to bring inside, this gets rid of the smaller bits and some of the dust. The only thing is baled sometimes can be a bit dustier, it depends on the time of year.
As for wires there is some info in the indoor housing sticky thread under bunnyproofing. I find it's best to use some sort of tubing and then tuck them away behind furniture or mesh panelling.