You’re not paranoid, right? It’s just that you’ve got some DVDs or CDs with stuff on that you don’t want to get into the wrong hands. How about shredding them with the Alera DVD/CD Shredder? The $70.00 device can cope with up to 30 discs a minute.
Alternatively find some matches and a fireplace and be prepared to sniff some noxious smells for a while.