I just switched from a strip-cut shredder to a cross-cut one and the mfr recommends oiling the cutters occasionally-- with a very expensive shredder oil they sell. The oil looks/smells/feels like the oil they sell for Hunter Original fans which I understand is just a generic light weight non-detergent oil.
Wonder if I can just get a quart from the local auto parts place and use it instead of the expensive stuff-- or do you really need to lubricate the cutters at all? I never lubricated the strip=cut shredder and it did just fine...