My kitchen steam and a/c

I need to get some form of ventilation for the study room. My study room is just not set up that good. I have the stove and microwave right over top of each other. When the stove steam rises, the condensation forms on the microwave and then drips back down. The steam from our cooking goes even higher. It rises up to the ceiling and leaves little water spots up there. I do not like how moist and warm it gets when I cook. I recognize the reason it is so poor is because I have no airflow in the study room. I need air conditioner or at least a fan moving around the air. The steam needs to be wafted around and the air should be frigid when I cook. The problem is that when our home was set up, the study room was originally in a unusual room. My husband and I expanded our home however forgot about Heating and Air Conditioning. There are no air ducts in the study room or open air vents. The two of us just made a solid room that is sealed from the rest of the house. Because of this, we can’t attach the current Heating and Air Conditioning unit to the study room. What I will need to do is buy a ductless mini chop for the study room. This will give both heating and cooling function and its own separate control unit. It will be extravagant however it is the only way to have airflow and climate control in the study room area. Sure I could go cheaper with portable Heating and Air Conditioning, however it would not work as good.