Razor edge...
On an axe/hatchet??? Are you planning to shave with it??? You can do it but the razor edge won't last, if you're cutting wood or anything like.
For a razor edge, you need: (1) Consistency of angle. (2) Fineness of grit for the second and third stone to be used. (3) Strop at the end.
I've started learning to sharpen with a belt grinder, and the finest grit I usually use is 15 micron. On really good steel, I'll go down to a 9-micron grit belt. Also have a felt belt to use with white rouge, then finish up with a leather belt as a strop. I can get any knife from a hard Buck to an El Chinese Cheapo, spooky sharp.
Any leather will do as a strop. Certainly an ordinary pants belt can be used--start with the rough side, end with the smooth side of the leather. Some people use a cardboard wheel, even.
As to requiring excellent steel for a razor edge, in my moderate experience, a fine edge can be put on just about ANY relatively thin piece of metal. (Or even non-metal--most people have suffered a paper cut or 2--PAPER, fer cryin' out loud!) On good steel it's easier, and the edge lasts longer in use.