“Gadol,
If a frum woman from KJ or NS (where driving by women is generally discouraged)”
What do you mean by “discouraged”? Are they against being an official owner/steady driver of a vehicle as a “kevius” and have no issue with non- Kevius (the logic can be, as I think Rav Wosner writes, that the issue is the circumstances that driving can bring to…which is not the case when driving only when really necessary).
In any case, theoretically speaking, it will depend what the Minhag was in the first place. If it is a Tznius issue then I don’t see the diff of being OOT has to with it.