T.O.F & bgf
First, in order to harden/case harden the surface of mild steel one must add carbon. Not to be too much of a smart a--, but that is 3000 year old technology.
I personally have NO knowledge of using sugar, saltpeter and chromium oxide. Makes no sense whatsoever to me. This of course does not mean it won't work, it does mean that I won't bother with it.
I DO know how pack carburizing has been done commercially in the 18th through 20th centuriesa. It always meant packing the parts in some form of ground up charcoal or soot. 200 years ago, or today, commercial guys are interested in speeding up this process or in some manner making it more efficient. Some rather carefull work by an 18th century Frenchman showed that sea salt and pigeon dung helped. For real. Bone charcoal is what can give pretty case colors, I personally suspect it began to be used because it sped up the process, or make it more uniform, colors being a nice secondary thing someone observed. A couple decades ago pack hardening compound could still be obtained from Park Chemical. They, and other 20th century guys, added barium carbonate to the charcoal make the process go faster.
Wood charcoal, the stuff actually made from a tree, think they call it "Cowboy somethingorother" is pretty @!*% available at the grocery store. Or, one can use the stuff pet stores sell to filter water for your aquarium.
The popular brand of charcoal briquettes includes petroleum coke, which means it contains sulfur, which will do you no good. I do recall that the last barrel of Park Chemical case carburizing compound, bought from Canada, had the smell of sulfur & I would not chose it for delicate or finely finished work. Yes, I know this from sloppy experience.