I don’t know if not showering is a kulah. While in his teshuvah Rav Moshe says “beemes yeish lehakel,” implying a kulah, the Aruch Hashulchan just flat out says showering is muttar. ????? ?? ????? ????? ?????, ??? ????? ???.
Also, I saw s source online b’shem rav moshe soloveitchik that our minhagim during the 9 days are copied from minhagim during sheloshim. Because the shulchan aruch says the minhag during sheloshim is not to shower, the minhag also developed not to shower during the 9 days. Now that there is no minhag to not shower during all of sheloshim, maybe the minhag by the 9 days changes too?