I had the same "musty" problem with the antique sewing machine that I bought a couple years ago. It has wooden drawers, and they were horribly musty. ...I'm trying to remember what I did to get the odor out....
Oh yes. I somehow got the notion to use boric acid on it. It was a horrible mess! LOL. I'm not sure how much it helped to tell the truth. If I were to do it again, I'd probably wash the thing down with a baking soda in water solution, or a light bleach solution.
What definitely did help, was that I followed up by oiling it with high quality furniture oil. I used tung oil, and I wonder if it may have had an anti-fungal quality, because there's not a trace of mildewy smell now. Tung oil has a strong smell, but not a bad one, and it fades. In any case, the wood looks great, and loved the oil...and no more smell!
KnittingHelp Queen Bee
It is not because things are so difficult that we do not dare; it is because we do not dare that they are difficult.