The basic discussion as shown below is not a matter of Kol Isha. It is actually a matter of the customs of the community. Thus the answer to your question would be that Kol Isha is not applicable to a woman saying kaddish. The articles linked below show the actual reasons for the discussion.
Since Kol Isha is not applicable, there would be no discussion about it.
For example Women Saying Kaddish which does not allow women to say Kaddish at a shul, does advise saying Kaddish at a private minyon. If Kol Isha were a problem, this would not be allowed either.
Women and Kaddish actually points to the original objection in the Chavos Yair for a particular case in Amsterdam. That article states that in a normal case (as in the question), there would be no problem reciting the kaddish with a minyon.
Women and Kaddish
Question: May women recite Kaddish in the synagogue?
Response: A contemporary compendium on mourning practices is the
anthology written by Rabbi Chaim Binyamin Goldberg (P'nai Baruch,
first published in 1986) and translated into English under the
ArtScroll title, "Mourning in Halachah". Concerning the issue of women
reciting Kaddish, Rav Goldberg notes the following: "If the deceased
left only daughters, although some have permitted a daughter to recite
Kaddish at a prayer service in her home, virtually all other Poskim
disagree and rule that a daughter should not recite Kaddish even in
her home." (Mourning in Halachah, chapter 39:21, p. 359) Thus it would
appear that halakhic authorities are generally opposed to women
reciting Kaddish whether at home or in the synagogue.
The difficulty with this pervasive negative halakhic orientation is
that it fails to take into consideration the rulings of the three most
influential halakhic sages in America. Indeed, it is openly recognized
that the rulings of the following three rabbis permeated the essence
and formed the standards of synagogue life in America: namely, Rav
Yosef Eliyahu Henkin, Rav Moshe Feinstein and Rav Yosef Dov
Soloveitchik.
Rav Henkin (1880-1973) was the Director of Ezrat Torah, a relief
organization for needy rabbis. Each year, he authored and published
the popular "Luach" for synagogue life wherein he detailed halakhic
practices. He was deemed the "Posek haDor", the decisor for issues
impacting on synagogue life. Concerning women saying Kaddish, he
wrote: "The question as to whether a [bereaved] daughter may recite
the Kaddish is bound up with her observance of the Sabbath, kashruth,
and the laws of family purity. If she does keep these basic mitzvoth,
it is permissible for her to say Kaddish in the women's gallery while
the men are doing so in the synagogue proper." (Teshuvot Ivra. The
entire text of the teshuva is translated by David Telsner, The
Kaddish, p. 301.)
Subsequent to Rav Henkin, the halakhic arbiter for American Orthodox
synagogues was Rav Moshe Feinstein, of blessed memory. In a posthumous
publication of his responsa, the following is reported. Rav Moshe was
concerned with whether it was necessary to have a Mehitza separating
the men and women sections for prayer, in the event that there were
only one or two women . He notes: "Throughout the generations the
common custom was for a poor woman to be in the Bet haMidrash to
receive charity, or as a mourner to recite Kaddish." His response was
that a Mehitza was necessary even for one woman [who attended] on a
regular basis. On an occasional basis, it was not necessary, should
only one or two women be present. (Iggrot Moshe, Vol. 8, O.H. 5:12b)
Note the terminology and the concern. Rav Moshe does not question the
propriety of the woman who comes to the Bet haMidrash to recite
Kaddish. He seems to assume that there are no halakhic qualms at all
with such a function of women at religious services. The only problem
is whether there need be a Mehitza during her recital. Indeed, it is
apparent that Rav Moshe accepts a woman reciting Kaddish as a normal,
unquestionable practice.
For many thousands of students of Rav Yosef Dov Soloveitchik, of
blessed memory, (former Rosh haYeshiva of Yeshiva University, and
halakhic authority for the Rabbinical Council of America) a halakhic
ruling from him was deemed authoritative. It is reported that Rav
Soloveitchik ruled that is was permissible for women to recite Kaddish
in synagogue. (cited by Joel Wolowelsky in a letter to the editor of
HaDarom, vol. 57, Ellul 5748/1988, pp. 157-158.)
It is important to note that the ruling of the Havot Yair (1638-1702)
cited by the Pit-hei Teshuva and the ArtScroll translation is not an
accurate rendition of the actual position of the Havot Yair. The
following is a full translation of the responsum of Havot Yair:
[translation not included for space reasons - see article]
I suggest that many may have misread the concerns of the Havot Yair.
He was not perturbed by a woman reciting Kaddish at a regular minyan.
Note that the case was not dealing with a regular minyan for daily
services, but related to a very unique request. It was for a minyan to
learn Torah in a home and for a woman to recite Kaddish subsequent to
the learning. It was, therefore, an unusual request. It was as if it
was not important for the daughter to recite Kaddish at a normal
minyan for morning, afternoon and evening services. The only concern
was for the daughter to say Kaddish after a special Torah learning
session. This was deemed a denigration of the normal recitation of
Kaddish. To permit this and not be concerned with saying Kaddish after
a regular daily prayer was tantamount to giving people the right to
make new customs and disdain the old. Accordingly, the Havot Yair
opposed such a practice. However, should a daughter pray in a regular
synagogue and recite Kaddish together with the other mourners, perhaps
even the Havot Yair would permit such a practice for the reasons he
himself articulated:
