Worrying about opening the fermenter is a little paranoid........
After all, you only need to open it long enough to allow the aeration process to happen. Some do this once a day (me), others twice, some even 3 times a day, but only for the time it takes to move fro the starting gravity to the 1/3rd sugar break.
The rest of the ferment time, there is positive pressure within the fermenter which prevents the ingress of airbourne nasties....
In any case, the main point is to get some air/O2 in to help the yeast development, but a side effect of stirring, is to mix up any particulates, which creates nucleation points so the dissolved CO2 (as carbonic acid) attaches and passes out of the batch as bubbles. It also, by removing the CO2/carbonic acid helps reduce the pH swings.
So, while the use of pure O2 is impractical here (cost and accessibility), I couldn't say how long you should add O2 with the stone, though is have thought that if you stirred it for q couple of minutes to remove the CO2, then bubbled the O2 for a couple of minutes, down too the 1/3rd sugar break, you should be fine.......
The usual hygiene practices should be observed for anything that you put into the must, so you don't introduce any spoilage organisms by accident. If something gets in by airbourne means, then "C'est la vie". It happens, but it hasn't happened to me yet....... in about 7 years of mead making.......