We were there a few years ago (sounds like the same cruise as Westcoaster with Nuuk being canceled due to weather). In Nanortalik, besides at the museum there was a public toilet in the tourist office and then a toilet if you paid to go to the event in the community center. I don't recall one either way in Qaqortoc. While waiting in line, more so in Nanortalik where the long line was steady, they handed out hot chocolate. In Qaqortoc the line to get back on board seemed to be up & down so if you timed it right you didn't have to wait long.