ItcheSrulik
i don’t know what you mean with “lmaaseh its a shirt”. For shatnez it needs to have function. And, another possible reason for it to have fuction, is because if not it wouldn’t be a day beged (see the third post on this page for more detail about that if you want).
I don’t know about your question from hilchos shabbos. maybe the halachos of a beged in regards to carrying have different guidelines.