when you mentioned exterior walls, you mean inside walls on the exterior of the house right?? Not outside the house walls?
Well, you could go directly to the plaster walls, but, you want to be sure not to hit air and not to hit any wires or plumbing. I would find the studs and mark them on the ceiling and then screw to the studs.
I would NOT use furring strips, this would be easier, but it would make your walls encroach into the house more and you would have all sorts of issues like doors, fixtures, elect plates and such. I would use green board or even cementious board in the bath for moisture protection.
Copper water lines run close to the studs in places and you could puncture that copper and not leak for months until the fastener rusts off and then the water pours out. be careful with this.