This worked for me on a slightly musty smelling 14-year old accordion: I put it in a closed box with camphor. Camphor kills fungus and bacteria and it also prevents metals from corroding, so it is good for the reeds and other metal bits. Mechanics put it in tool boxes, and it will prevent silver jewelry from tarnishing. I put two pieces of camphor in the box. Each piece was about the size of a Smartie, so you don't need very much. The camphor slowly sublimates (like mothballs). It lasted about 2 weeks before I had to replace it. After a month the musty smell was mostly gone.
I also put camphor in the soft-sided case which took about 2 weeks to completely get rid of the smell.
I try to play it every day, and when I do I put a tiny amount of Vicks VapoRub on the back of my hands. Vicks is 4.7% camphor by weight, so the idea is that some of the camphor gets into the bellows when I'm playing. Maybe it does nothing, but it doesn't hurt, and it masks the smell.
One of the best disinfectants that people don't generally know about is hypochlorous acid (HOCl). Sounds dangerous but our white blood cells produce it to kill microorganisms and I think you can safely drink it, but that is best left untested. Water is H2O. Replace one hydrogen atom with a chlorine atom and that is HOCl. Is is about 100 times more powerful than chlorine bleach at killing microorganisms, and it is effective at killing spores which bleach is not good at.
https://www.eurekalert.org/news-releases/581270
HOCl is also better than rubbing alcohol and iodine for cleaning wounds at a concentration of only 6 ppm:
Hypochlorous Acid: An Ideal Wound Care Agent
Why don't you see it everywhere? Because it has a short shelf life. You have to make it and use it within a few hours or a few days depending what you read. I've been using it for years for smelly dishwashers, smelly drains, fungus on window frames, etc. There are expensive machines that make it from water and salt. I mix 1 teaspoon (5 mL) of bleach in 1 litre (1,000 mL) of water, and then I add 1 teaspoon of vinegar. That produces a 200 ppm solution of HOCl which is good for spraying on surfaces. Use 2 litres of water and you will get a 100 ppm solution which is good for soaking things in. I only let it work for 10 to 20 minutes because about 20% of the bleach does not convert to HOCl, so it will have a bleaching effect if you let things soak in it for a long time.
For the musty accordion, once a week I put about 2 tablespoons (30 mL) of the 200 ppm HOCl solution in a small glass jar and put it in the box with the accordion along with the camphor, and leave it in the box overnight (24 hours maximum). The idea is that HOCl gas will help kill the fungus. I don't know if the small amount of HOCl gas will corrode metal, but the camphor should mitigate that. I haven't noticed any corrosion anywhere.