A Shaliach Tzibur who is an Avel praying in a synagogue with a different Nusach

First question:During the year of mourning, someone who follows the Ashkenazi custom according to the Rema wants to lead the prayers in a shul where, according to its rules, they daven Nusach Sefard. Should he avoid - when reciting the Kaddish Yatom - the words that appear only in Nusach Sefard? Skipping those parts wouldn’t go against the shul’s rules.Second question:Is it better for him to avoid being the shaliach tzibbur in such a place altogether, and instead go somewhere where the chazzan davens according to his own (Ashkenazi) custom?Thanks very much.

Shalom,

He should say the Kaddish according to the custom of the place.

This is not a reason to avoid serving as the chazzan.

However, ideally, he should daven in a synagogue where he can follow the custom of his ancestors.