We visited both of these ports last summer. They are very different to a typical cruise port. Small settlements with very little infrastructure, so don't expect lots of tourist shops. In terms of currency Danish Kroner (the official currency), Euros, and US $ were all accepted.
Qaqortoq does have a tourist information shop next to the tender dock which sells some souvenirs. There is a large shop a short walk from the dock whish is advertised as selling local furs, although we did not visit so I cannot really comment on that. There were a few local craft stalls set up with locals selling hand made souvenirs. It was also possible to book iceberg "safaris" by rib boat from the tourist information (we had an amazing trip seeing icebergs up close).
Nanortalik is even smaller, with very few shops, although again, some locals selling craft items. There is also on open air museum which we really enjoed.
However, the real enjoyment of these two ports is simply to wander and get a sense of the beauty and remoteness of these places, which are unique. The scenery is stunning, and the locals very friendly.