What can I use instead of a ducted range hood in my kitchen?
One solution is a window extractor fan.

Cutting a hole in the wall is pretty permanent, but you can always replace the glass in a window if you need to restore it. Actually cutting a hole in the glass is a job for a professional, but it's pretty quick and doesn't make much mess.

Any room with a gas burner (like a cooker) needs a vent to allow fresh air in, otherwise you'll use up most of the oxygen and it'll start producing poisonous carbon monoxide. If you add a fan to suck air out of a room, it's even more important to have a vent to allow fresh air in.