Rust blueing is within cost at home of dang near anyone. Polish axe head to 320 grit. This is the most important step. Degrease till it's spotless. I use purple power then biol in tsp. from this point on you can not touch it, wear latex or white cotton gloves. There are several solutions for about 15$. I like brownells slow rust formula. You coat the metal in the solution and wait about 12 hours(really depends on your local humidity) It will form a fine rust. Boil in distilled water converts it to black oxide. Then you use 0000 steel wool (that's been degreased as well) to card off the velvet fuzz for lack of a better term. Repeat this at least 6 time(some modern tool steels take many more cycles). Once you start you can't stop. Letting it rust longer than what it takes to get a very fine rust cause pitting and ruins the look needing polished out and restarted. The look is a beautiful blue/black with a satin sheen like no other. This is how high end double barrel shotguns barrels that are soldered together have been blued as well as other high end custom rifles. It's 6 times as durable as hot salts blueing, maybe 20 times as heat/nitre blueing, and a thousand times as durable as cold blueing(which is quite worthless). After last rubdown with steel wool warm steel up till it uncomfortable to handle and oil generously with boil linseed oil. Wipe most off quickly(but don't rub down) and let set a day or two. Rub with a soft cloth and enjoy.