Mid Sept should be fine. A few years ago I did a southern Sweden and Finland trip late August into mid September, and the weather was great. However, the Swedes really consider Sept 1 to be the end of summer, and some of the schedules changed for touristic activities, so you may want to see if that is true there as well.
Its been a decade since I went to the Baltic countries, and was July when I went. All three capitals are worth spending a few days in.