What you are looking for are shallow hardening steels. Another way to look at it is how fast they need to be quenched. Any steel that can be quenched in water can be lamellar (pearlite) annealed in wood ashes, vermiculite, lime etc... Oil quenching steel can start to give you issues, which brings us to 52100 and 5160... these steels can be softened by the wood ash treatment but they will not form pearlite as course as what, say 1095 will. It may be knitpicking but for future refference 5160 an 52100 are not simple carbon steels, but rather alloy steels.
Off the top of my head here are some steel that can be easily annealed with simple methods- 1060, 1070, 1080, 1095, W1, W2, 15N20 and a few more I am not thinking of. They all have something in common- very few substitutional alloying elements to facilitate deep hardening. The simpler the steel, the simpler the techniques to succesfully work it. Any stainless capable of hardening in air will simply laugh at wood ashes.
