I like to use a Sharpie marker. Cover the sharpened edges, it protects until the next time you need to check the edges or touch-up.
Also a cold bluing pen or dye, and even some Feibings leather dye would work.
Don't like to use the oils, vaseline, or such, because of the dirt it attracts. And messy!
As for cleaning the rust off, one of those toothbrush style wire brushs work good. And resharpening should clean up the rust.
Welcome to the fun side of archey, and good shootin too ya!
Steve