Unless you are hearing symptoms of leakage in the high-impedance node, I would not touch it.
Symptoms would include random noise and hiss, perhaps made worse by gently exhaling on the area (to temporarily increase the humidity). That would indicate that the "nasty gunk" is causing leakage.
If you do want to try cleaning it with distilled water I would use a new, clean, soft toothbrush and dip the ends of the brush into 1-2mm depth of water. This will keep the amount of liquid to the absolute minimum. I would repeat several times and rinse the brush in distilled water between each brushing.
Remember that until the water is completely evaporated, the microphone may be very noisy, low-output, or maybe even not work at all. If you have a heat gun or hair dryer, you could accelerate the evaporation, but this is VERY RISKY because excessive heat could damage many parts of the microphone including the microphone capsule itself. I certainly wouldn't approach the microphone any closer than 500cm with a heat gun or hair dryer. Better to just put it out in the sunlight to dry out. Of course you wouldn't want to subject it to salt spray from the ocean, etc. No matter where you are in the Maldives, you can't be very far from the ocean.