I've had a quick look through 'Firearm Blueing and Browning', by R H Angier, dating from the 1930s, but still available as a reprint, from Stackpole Books (USA). This is the 'bible'. However, it shares that book's disadvantage of not having an index, so searching is a pain, and I might have missed something. I have found reference to wax being used only as an after-treatment, to provide corrosion protection. Like shoe polish, and the Karate Kid, 'wax on', then 'wax off'…
The book's a bit of a nightmare, because there are so many ways to produce the magnetite oxide on steel, varying from tedious hard work via alchemy to simple stuff. There's little guidance on their relative merits and the chemical nomenclature is obsolete in many places.
Cooking up in a boiling solution of 80oz sodium hydroxide and 50oz potassium nitrate in 1 gallon of water (sorry about the units) is easy and effective – and rather nasty… The desired boiling point is 140 C, and is adjusted by the amount of water. Since the water tends to boil off, you may wish to add more at some time. Beware! The colour develops rapidly. Rinse well, dry and oil. Like electroplating, surface preparation is everything, and thorough degreasing is vital. Solvent degreasing tends to leave residue: hot alkaline detergents are the way to go – and keep your hands out of the stuff!