Chosson:
So I took a look at the Mishna Berurah in Simin Beis, and you do have a point, even though I am not sure if it would apply to anything you would walk around with in public (if not for Ervah type Tznius).
I suggest one asks their own Rav. But thank you for correcting me.
The key here is “Kol Ma Shedarko L’heyos Mechusa L’OLAM”. IIRC, there is a question if this includes an undershirt in this time period.