I recall a similar thread on one or another instrument forum. You might search for it here or on Mandolin cafe. I have had good results in the past with a couple methods. Of course, test on an inconspicuous spot on the guitar before going all out!
Apple cider vinegar is an excellent mold killer and should be safe for most finishes, particularly the newer ones. As I recall, the forum also spoke about using a diluted bleach water solution (exact ratio alludes me, but as I recall it was quite weak). I mixed up a batch and it did a very good job on a vintage parlor guitar I was working on that had significant mold issues. In that case, the mold and mildew were on the inside of the guitar. I had to pull the back to fix it so I was able to lightly brush the bleach water solution on and wipe it off with a damp paper towel after it sat a while.
In non instrument situations hydrogen peroxide also is an excellent mold killer but I can't say how it would react to finishes, particularly nitro cellulose of shellac.