i used to live in a serviced appt and found a similar thing, though that was b/c I had the a/c turned "down" to 22-24degreess instead of the 18deg the service staff repeatedly set it to. at 18deg it was like an icebox, at 22 deg it was nice, but mould came. it was so bad that even papers on my desk would droop when I picked them up, and my suitcase went all powdery on the outside.. yum yum...
i ended up buying an electric dehumidifier, they drain about 200watts and only run when the humidity reached a certain level (with an analogue dial, you can set that with trial and error). the downside is you need to keep emptying the water catcher (and it is horrific how much water they pull out of the air) or have the drain pipe pointed into a floor drain for constant drainage.
there's no point just focussing on your cupboard - the problem is throughout the appt, unless you seal the cupboard and rarely open it.
the downsides of the dehumidifier is they generate 200w of heat (or whatever their power consumption is), which is no worse than a few light bulbs, but you can feel the warm air coming out.
upside is 200w is less than 1/10th the cost of the aircon, even if it runs all day long