Is it safe to use portable mini evaporative air coolers inside a yacht?

Usually, boats use de-humidifiers while in extended storage.

A complete Joke......they will add heat (space will become warmer) and a higher temperature holds more moisture (humidity). To tired to explain thermodynamics tonight.

Why not just run the air con system? If you want to reduce load set the Tstats at higher settings. Here in so fl we run the air con 24/7/365

You don't have a ISO transformer?

The transformers should help on those quick spikes, but for longer sags, you may want to make some adjustments to the boards;
Time delay before restarting the compressor.
Low Vac cut off also.
Maybe even soft starters.

Not trying to be a S A, just offering some help on those boards.

Uninterruptable power supplies (USB) battery pack and inverter like those small ones sold for pcs and electronics. They cut out the spikes and make up for low voltage (brown outs) using battery's. They can be designed and installed for a entire boat. A voltage and frequency study should be done to find out what the problems are and how far from specs.

You should be already using these on all your electronics, Radios, PCs, TVs etc.

Meant UPS above ,not USB

some are vented to the outside?

Your probably looking at a portable AC unit that has a 4 to 8 inch hose run outside , like a dryer hose , That's where the rejected heat goes.

That exact same unit the OP posted would be marketed as a humidifier in colder climates. Technically a passive humidifier as opposed a much better heated humidifier.

Swamp cooler is pretty accurate. Huge heat wave the last ten days in GA where I have a farm so I had to install a 12,000 BTU Haier portable A/C and dehumidifier in the master as the other wall units weren't cutting it. I vented the exhaust out the window and installed a drain line and @ 70 degrees and holding for eight hours with the bed room door closed I had 80 % humidity. Certainly cool but certainly damp. I would never install one of these aboard due to venting and condensate drains besides the fact when in cooling mode they don't remove moisture from the air but rather add substantially.

The portable AC units with an intake and exhaust hose would work, but a porthole or hatch would need to have a temporary surround piece fabricated for it. Condensate drains would need to be run as well, but with little humidity it shouldn't be much water flow.
How about a 'window unit' installed in a temporary location over a hatch. Would be ugly and take some minor fabrication of a hood or surround. But one or two of those could run constantly with no seawater needed and when a power spike blows them up, go buy a new one for less than the cost of a circuit board for marine units. Obviously only a good idea for when the boat is not in use.

TK minds well just run the AC already installed. His only option that would be better is keeping his boat in a sir conditioned boat house/shed that would also stop solar damage to the exterior.