I'm not sure if these are the same as the polishes I used several lifetimes ago in the jewelry industry or not, but back then from coarsest to finest, we had:
Black or emery, this stuff worked on everything, but we almost never used it, cause it would cut through plating in a fraction of a heartbeat... not good, especially when someones prized piece was dropped off for a polish, and they didn't know it was plated. Most jewelers wouldn't have this in their shops for fear of accidentally having it loaded up on a wheel and destroying something.
Brown or tripoli was next, this worked on everything (except platinum and things with nickel including chrome), kind of all purpose, I used to buy it in 2 lb cakes. It really worked nice on bone, horn, and hard leather. I rarely worked in steel, usually sterling silver or gold, but this is usually what I started with (and frequently ended with).
Then came white, the next step up, and again pretty universal like the Tripoli, except only metals, no bone, horn, wood, etc.
Next was the green, which was again like the white only finer, again metal use only.
The last was red, which was finer yet, I never used it though, white and or green always got me to mirror shiny.
I'm not sure, but I think Tripoli, white and green would be the most useful for tool steel and stainless.
Store these in an air tight container (zip lock baggie is fine), the wax the abrasives are loaded in will dry out if you don't. It'll crumble when it gets too dry, and you won't be able to load it onto a wheel (or strop).
These are for polishing, I'm not sure how effective they'd be on the edges of our current wonder steels. I actually use the flexcut gold on my knife strop which is leather mounted to hardwood, it cuts a lot more steel than any of the jewelers rouges. It's almost funny how fast it'll "polish" my gold wedding band.
I didn't have the fine motor control to use a barbers strop, unless I pulled it really tight, I'd wreck the edge with it, so I gave that up.
If you really want scary sharp, I'd look into the diamond stropping pastes the straight razor folks use, not sure how practical they'd be for a field knife, sharp enough for a comfortable shave is a lot sharper than I ever take my knives (popping hair off your arm is a lot less sharp than a smooth comfortable shave). Of course that's apples 'n' oranges as the blade geometries are different.
Erik