If someone purchased a new shirt before the 3 weeks, and the shirt arrives during the 9 days. Can someone try the shirt on just to see how it fits, but will not wear it? Can one wear it on shabbos?
Yes, and yes.
The problem in the nine Days is to wear a new shirt, not to try it on.
On Shabbos it is permitted to wear the new shirt (and henceforth it can be worn on Sunday too, since it isn’t new).