I have a couple different options for mining locations, but right now a hole large than 20x20 would be extremely dangerous in my opinion. I don't want anybody (or anything) crawling through it to get to me or my stuff. The hole should match the size of the exhaust fan, is that right, generally? I know the sucking capability calculations are going to be more accurate, but just for estimation-sake.
It does not need to match, for example, start with only one exhaust fan, if is not doing the job well then add another one and so on, if your exhaust fan is 50x50 then start with 3 holes 20x20, do not place the holes closer, thieves could find a way to link/connect them. After you do the first then you will understand it better cause theory is something, try it outs and see how it actually works is something else.
Air Conditioning won't do much good if you don't move that hot air out while the cool air is coming in it's about air flow and how you move it an were.
so that said
Air Conditioning if used right is very safe if you can afford to do it in other words it's the most costly way to do it . or not worth it unless your rich or have no power cost to worry about then it is very safe to do and the best way imo to do it but that's a debate so it's all about what your willing to invest and can afford till you see that ROI, if that's what your after .
3.41 btu per kwh is a lot, I'd say, air conditioner is the safest and expensive, approximately which all depends, only one exhaust fan does the job of 5 air conditioners and uses only 300 watts hour instead of 5000 watts hour, so is a huge difference.