The Shabbos Mincha Nusach is very simple; the same tune is used more or less for everything except Ata Echad.
But not wearing a tie is not a chumra. It is a practice I see as being very warranted and corroborated by the sources.
I don’t wear a tie anyways on Shabbos, although wearing loud and flashy ties seems to be popular among the yeshivishe velt these days.