I daven Nusach Sefard, and my minhag is to have Shofar in middle of quiet Mussaf. After Shofar the minhag is to say Hayom Haras Olam before continuing. Even on Shabbos when we don’t blow we still say Hayom Haras Olam. When I am davening in nusach Ashkenazi minyan where the minhag is to not blow, should I still say Hayom Haras Olam?
When davening in a minyan that davens with a different nusach than yours, R’ S. Z. Auerbach zt”l used to say that whatever is meant to say quietly, you would say according to your nusach. However whatever is said out loud, is said in the nusach of the minyan that you are davening in. Therefore the quiet Shemona Esrei would be said the same way you would say it in your shul. If your nusach says Hayom Haras Olam in the quiet Shemona Esrei when Rosh Hashana is on Shabbos, then you would do that even when davening in an Ashkenazi minyan.
Kesiva v’chasima tova