I respectfully disagree. Those so-called "Safety Knives" cause more accidents because the same companies that are ultra-paranoid about liability tend to forget that the razor blades inside the "Safety Cutters" need to be replaced from time to time. The length of the blade also makes things MORE dangerous from my experience because it is so short, 1/8 Inch, it won't always cut the cardboard the first time. The relative dullness of these blades (in terms of cutting tough materials all day such as cardboard) combined with the minimal blade to work with, make it more likely that a worker will slice his or her own hands. Several people suffered from cuts, some of which were deep, at a factory I worked at several years ago.
I ran into a similar situation back then as the OP is finding now. Kept my knife in my pocket and used it when I really needed to. My safety, I.E. not slicing through my fingers/veins was paramount, especially when the lawyers and corporate types have never worked in a non-office setting.
As for the above post, box cutters are like "Safety Cutters" in that the replaceable blades dull and are not switched out. While a box cutter has a longer blade to work with, the edge is far thinner than a normal pocket knife, and therefore has more "give". This "give" means that like a "Safety Knife", more force must be applied downward to make the cut. When the blade is not doing the cutting, you run the risk of cutting yourself. Simple edged tool 101.
And yeah, It's their company, but it's still your fingers/limbs/veins/etc. Find a job where you are respected as a worker, not treated like a chattel.