When we were first planning this trip, I remarked to Chris that it will be weird to travel somewhere with no options for local dining or shopping.
I spoke too soon. As it turns out, there is a gift shop on Antarctica.
Palmer Research Station - which is on our itinerary - has a gift shop that supports the station's social activities. They sell t-shirts, sweatshirts, sweatpants, postcards, coffee mugs/thermoses, water bottles, pins, patches, hats, and magnets. They sell postage at the store too, so we can send postcards right from the station. And everything is duty-free.
Wherever you go, there's an opportunity to get a t-shirt.