Most cold blues like 44-40 Numrichs brand are an acid (selenic?),,I'd go the other way and use an alkali like bicarb/soda or wash it with soap and water.
If I do use that stuff at all and that is rarely, I simply wash & scrub the part(s) with an old toothbrush and common dishwashing soap,,then rinse. Seems to take care of the acid residue. But they will need oiling of course to protect them.
Vinegar is a decent blue/rust remover as well so it may put you back to step 1.
If you're using cold blues like 44-40 from Numrich and the other common types,,they do have a very distinct smell,,and not a good one by most peoples standards! 44-40 does after rust.
Brownells OxphoBlue cold blue does not after rust and none of the 'smell'. I prefer to use it if I use a cold blue for anything.