The cooler in the linked video lets ice met. You could just put the ice in some tank with added ribs and suspend the tank under the roof. More silent, more reliable.
If you replace melting by evaporation, you will have a vapour in the room. Do not use alcohol, as the explosion risk is strong, and it's a poison. Vinegar has only drawbacks over water. As a melting solid, water ice would be my choice too.
Your kitchen freezer has at least its heat sink outside the room I hope? If the whole freezer is inside, it will produce more heat at its sink than it absorbs heat from the water it freezes.
If significant modifications are conceivable, you could transform a (cheap old used) fridge into an air conditioner. Its heat sink must be outside and its cold part must communicate with the room, possibly by removing the door and blowing air in it.
I suppose you already tried a ventilator?