High powered at the top, passive intake at the bottom. An axial fan will struggle to shift air through a carbon filter, and if you move air out, more air will enter, so long as you leave somewhere for it to get in. Air can only flow through the room as fast as it is being exhausted, there's no point trying to blow more air in there.
As for your original problem of how to ventilate it, work out where you can put the cabinet next to something that you can run ventilation through, whether it be from the back, side, bottom or top. Your ducting has to go somewhere, once you figure out where the stale air is going, and where the fresh is going to come from (they should not be the same place) then it should be fairly obvious where you have to cut your holes for achievable stealth.