Train your cat? Seriously.
Yes, they're curious and will get into things (cardboard boxes of any kind are like cat-magnets in my experience), but you just train it not to do that kind of thing and/or keep away from things you don't want it to touch.
When my ex's cat (now my cat) scratched the white leather sofa she had, within a week the cat was trained not to sit on anything sofa-shaped or white at all. To this day, 10 years later, that same cat will huddle into the tiniest, tiniest space on top of a coloured blanket on a white sofa, and not set one paw on the white parts. She also responds to "Down" (a generic "don't do that" command), "settle" (i.e. "I don't mind you sitting on me but get that tail out of my face so I can watch the TV") and a handful of other commands (not least, her name yelled in her general direction - but you do feel an idiot yelling "Star" everywhere. I blame my ex).
Sadly, this training back-fired slightly as her new home had a black sofa, but again a week later she was trained to sleep on her little radiator bed (which is also technically half-on the sofa) or a brown blanket.
Given that my cat is the DUMBEST cat in the world (from suicidal fox-hunts of epic proportions - we almost attributed that "largest fox killed" story in the news recently to her, until we read it - to just not recognising that meowing to go out on the door NEXT to the catflap won't get much done, or that meowing for food only to sniff it and walk off will not make your owners happy), I can't imagine that others would have too much of a problem training their cats.
If all else fails, connect your cat's collar to an earthing strap.