I've retrained myself to use documents in PDF from either a notebook PC or smartphone (Blackberry) and not carry around the paper. If copies are needed for presentations, I'll forward the PDF in advance. If I'm attending a meeting, I'll routinely request soft copy of the materials to be discussed.
While a shredder in the business center may be an advantage for those like yourself, my biggest concerns are twofold: First, the possibility of the increased liability due to risk of injury by having shredders in the room(s); plus the potential for unwanted vibration and noise which might disturb other guests. The risk of injury to children who come in contact with shredders is well documented in gruesome detail. Other than that, when I'm the road, quiet, tranquility and a restful sleep is my major priority.
Please Marriott, don't put a shredder in my room or remotely near it.