In Lithuania it was common for women to say kaddish, sometimes standing in the back (yes, at the back of the men’s section) to say kaddish for a loved one.
The common custom is to ask a man who does or can say kaddish to say it, and the woman says kaddish along with the man or men. The woman need not say all the kadeishim, certainly not the kaddish d”rabbonons.
It should not bother the men at all. If the men are not used to it, they will adjust to it in due time, it is not a big deal.