I wouldn't want my personal documents to go outside my control for fear of someone in the company doing random inspections. It risks being disciplined and not worth it.
Where I used to work there were shredding machines on each floor near the photocopier so I did take the odd few sheets in but not a whole bag of personal papers, that's CFery!
We bought our own shredder for odd sheets, and for a larger amount, we add it to our garden incinerator and it's a quick burn.