Scraps of cardboard for sure. Also little dumb leftover pieces of foam core. I used to put used box cutter blades inside the foam core scraps before throwing them away, thinking that was a safe way to do it. It's probably not. So now I just toss used blades into an old empty prescription bottle and just keep that on a shelf. (Therefore, I also hang on some of my prescription bottles).
I also tend to hang on to some empty plastic jars and food containers once in a while, too. I wash them thoroughly of course. I probably sound like a hoarder. I don't hang on to every scrap of this stuff, just a small amount. The plastic jars (like the ones corn starch come in) are handy for storing left over pieces and parts from various crafting projects.
I work in an industry that uses razor blades and if OSHA comes in and finds one laying around it's an automatic fine ($500 last I heard but that was a decade ago). They make disposable jugs for used blades, we put the blades in and throw the jug away once it's full. So, basically, the same as your method. It seems to be the best anyone's came up with.
Back in the days when Safety Razors were king, many houses had a little porcelain slot embedded into the wall by the sink, or one cut into the back of the medicine cabinet. This led to a completely open space in the wall, and the idea was that it would take longer than the expected life of the house to fill it up with rusty razor blades.