Won't hurt the tools themselves, though corrosion will dull your edge. One of those things like the common cold, where doing nothing gets you to the same place as dosing every symptom. Mechanical removal of the rust is fine. Prevention is NOT 100%, so I tend to go with the flow and clean up afterward on those things I can't isolate. The blue stains on your hands will respond to lemon juice pretty well.
Go through your shop and look at all cast iron you may have in line with the throw from the lathe, or even horizontal surfaces outside the throw zone. Brushing shavings off yourself can leave some ugly rust on the jointer table if you you don't notice. DAMHIKT
Oh yes, tannic acid doesn't make an acetate, acetic acid in the vinegar does. It's converted by the tannin in the wood.