When it rusts, oil it!
You can use mineral oil or any manner of fancy expensive waxes and coatings, or just WD40 if your'e not prepping food. You can apply it with lintless cloths, rags or wipe it on your jeans! A swipe with a rod, strop, stone or hone will clean up the edge well enough to cut timber.
Dont chuck it in a fire!!, if its too hot to touch you have likley ruined the heat treat!
IMO it will take about 500 years before rust defeats a decent axe or hatchet, I've seen 1000 year old viking pieces that were a bit pitted but a bit of oil of some sort and a half hour with a decent file and stone, would rival your average Gransfors, Fiskars, or even most customs!
An Axe, Hatchet or Tomahawk is a tool IMO, a perfect finish only improves performance in tiny degrees. If you want a shiny wall hanger then 420 stainless is O.K., gee I've got a cheapy ALDI hatchet in mystery 3 somthin?? "steel" That seems to chop without deforming.
Patina shows character!