Hello. My name isXXXXX can help you with your question. You are correct in that about Murphy's. In fact, I think that would make it much worse. Mineral spirits will almost certainly remove some of the finish. Ammonia can kill mold on the surface, and can require some scrubbing.
The best way I have found to remove mold, and may not even require touching the surface, is to spray it with a combination of bleach and water - about 1 part bleach to 10 parts water should be enough. Bleach is highly toxic to mold and you should see results very quickly. Just spray the surface of the mold and wait a little while. As with any cleaning method, I strongly suggest you try spot testing one or more of them to see which one provides the best result without affecting the finish. This is an important caution: Mixing Bleach and Ammonia produces Chlorine gas, which is deadly even in small amounts. So for this method in particular, you must spot test a small amount in a well ventilated area - if the surface was cleaned with ammonia recently (although not likely based on the mold) - it can be enough to react with the bleach. It is only because I (stupidly) mixed the two in a bucket once that I am acutely aware of the danger. If you are using bleach and you feel the slightest tingling sensation in your throat, leave the room and let it air out. I'm sure you've used bleach before, so I'm sure you don't need a lecture about mixing chemicals. When you use bleach in this manner, you should not have to wipe or rinse the surface. Just spray lightly, let sit, and repeat if necessary. If any dry mold remains after it is dead, you should vacuum the area with a HEPA filtered vacuum and/or proper respiration. Mold CAN be dangerous, and mold spores can still be dangerous after the mold is killed, especially when airborne. Again, just take common sense precautions.
Alternatively, or as a second form of remediation, Grapefruit Seed Extract can be used in a similar manner. The citric acid from the grapefruit kills mold and a small amount goes a long way. Since you are on a small island, you may not be able to find this, but if you have a health food/natural foods store there, it's a good place to look. You only need about 10 drops of grapefruit seed extract per cup of water - mix in a spray bottle, shake and spray. No rinsing is necessary.
These are the two methods of which I am aware that can kill the mold with no contact/scrubbing. Just spray and let die. In these concentrations, neither should affect the finish, but the only way to be sure is with a small spot test.
Please let me know if you have any questions, and I'll be very interested in knowing your results when you have a moment.