Found a vintage leather jacket with a weird musty smell—best way to clean without ruining it?

I recently scored a vintage leather jacket from a thrift store for just $15. It's exactly the style I wanted, but it has this pretty strong musty smell that I can't get rid of. I've tried airing it out outside for a couple of days and lightly wiping it with a damp cloth, but the smell lingers. I don't want to use harsh chemicals or soak it because I'm worried about damaging the leather or the lining. Has anyone dealt with removing stubborn odors from vintage leather jackets while keeping the material safe? Also, are there any home remedies or gentle products you'd recommend that actually work?