A 172 should be able to fly in the canyons; they fly everything else in them. But that needs reasonable local knowledge, at the very least.
I doubt a 172 would be able to go over the top, FL160 or so...
One can do it VFR; below Switzerland the airspace is Class C at FL130 so one
should be able to get transit. If one goes from Austria, one can go VFR up to FL195. But not in a 172
