You need to add heat to the server room. Enough heat to make the A/C work harder to maintain your set temperature, but not so much heat that the temperature rises above the desired range.
A well-designed HVAC system for a server room will include an air cooling device, a separate air heating device, a temperature sensor and a humidity sensor. If the air cooling device and air heating device are within the same air duct, the air cooling device MUST come first. During times of high humidity, the A/C will cool the air below the desired temperature and remove a lot of humidity, then the heater will boost the air temperature up to the desired temperature, resulting in much dryer air than an A/C alone can give you.
If you are using a mini-split HVAC and using the "Dry" mode, this simply reduces the fan speed to improve dehumidification. Ultimately, it will not give you the dry air that you desire. A standard mini-split is the wrong equipment for this room.
Try a one-day experiment: forget about "Dry" mode. Use "Cool". Set your air conditioner for the desired temperature, then plug in the biggest electric heater that you can safely run in the server room. Monitor the temperature and humidity. You will be pleasantly surprised. I predict that you will see a dramatic drop in humidity within the first 1-2 hours with no change of temperature.
The permanent solution is to hire an HVAC contractor that knows how to control temperature AND humidity, and this will involve both heating and cooling at the same time when it is hot and humid.