420hc fits in the "surgical steel" or "age-hardened cheese" category -- but all those cheeses can be sharpened if the right technique is used. Some theoretical understanding helps, so I'll explain the theory first....
The same phenomenon that causes difficulties in sharpening cheese also occurs in steel, but to a lesser extent. Steel is formulated, rolled or forged, and heat-treated to produce a product that might well be described as "crisp" -- when you rub a "crisp" material like steel against an abrasive stone the material tends to be ground away rather than smooshed around. When you grind it to a sharp edge, once the two edges meet there is some tendency for a very thin layer of the steel to get smooshed around and out past the edge rather than ground cleanly away -- that smooshed out layer is called a "burr."
Sharpening on one side smooshes out steel toward the other side of the edge. When you can feel a smooshed out burr along the whole edge, you switch to grinding the other side of the edge to grind away that burr. You can easily grind off most of it but you'll find you've smooshed out some steel while you were grinding and now you have a burr that's smooshed out over to the other side. Then you go to alternating strokes, one stroke on one side of the edge followed by one stroke on the other side. Each stroke does some grinding and some smooshing, but each stroke counters the smooshing of the stroke before. That reduces the burr until it's so small it's hardly noticeable and you might consider it acceptable and ignore it, but you can only get rid of that burr completely by stropping, even with the best and crispest steels. Always finish with stropping for best results.
Cheese, on the other hand, is not basically crisp in nature -- it is an inherently smooshy material. Knives are not made of ordinary cheese, of course; specially formulated cheeses are used in the knife trade, and they are age-hardened for a long time until they dry out and turn shiny and look and feel almost like metal.
Blades made of cheese are not called "cheese blades" in advertising, by the way; they are called "stainless steel blades" because cheese has little tendency to rust or stain like steel, and it sounds better. Not all "stainless steel" blades are made of cheese, but if it only says "stainless" or "surgical stainless" or if it says 420-J2, 420-HC, 425M -- those are cheeses. Some higher-grade cheeses for cutlery use are designated 440A, AUS-6, 440B, AUS-8, etc. They have smooshing characteristics midway between the low-grade cheeses and real steel.
No matter how shiny and metallic the cheese looks, when you try to sharpen cheese you find it has much more tendency to be smooshed around rather than ground away than a real steel. Grinding smooshes out an enormous burr of cheese which cannot be removed by more grinding -- you can make it smaller by alternating sides and reducing pressure, but you'll soon reach a point where you can't grind away any more of the burr. All you can do is smoosh it back and forth from one side to the other, and continued grinding will never remove the burr if you grind till doomsday.
That's when it's time to strop. The reason grinding can't remove the burr is the hone is flat -- it pushes the burr away and then it can't reach it any more. The strop is flexible enough to follow the burr; the burr can't get away from it. Just a few strokes on a leather strop is sufficient to remove the burr even on the lowest-grade, smooshiest cheese. Treating the strop with a fine abrasive polish such as tripoli compound makes it work faster, but if all you're going to use the strop for is removing the burr after grinding no compound is necessary; just plain leather will do it. If leather is not available, some have reported reasonably good results stropping on the kind of cardboard you find on the back of a pad of paper.
Using the right techniques, you can sharpen cheese just as sharp as real steel. Depending on the grade of cheese that edge may not last long in use, but you can get it just as sharp initially, and with no more trouble than sharpening steel.
Some people like to put a coarse edge on steel because it works better than a polished edge for some purposes, but cheese doesn't hold up well when you put a coarse edge on it. The tiny teeth break off too easily; cheese is not as strong as steel. However, you can put a coarse edge on cheese if you want to experiment: do all your grinding on a coarse stone or use a file, and then go directly to the strop without doing any polishing on hones first.
-Cougar Allen :{)