This is the route we took on 3-4 August. Below is the original description, from the planned route, which we didn't exactly stick to…

Furgler is one of Austria's most popular mountains, but most people approach it from the east. From the north the path should still not be technical, but rather less busy and somewhat shielded from the hot sun. Following that, we can pass three or possibly four 2500m+ lakes, and then summit the Witch's Head, Hexenkopf. Finally, we descend back to See.

This route starts from the valley in See. Alternatively, we could save 5 km each way, and 730 m ascent and descent, by taking the Medrigjochbahn (€12 up, €7 down, or €13.50 combined, I presume only in one day). Given the limited hours of operation, I think that making the last cable car down is almost impossible in one day, but the route could be split in two at the Hexenseehütte (€9 for young DAV members) or Ascherhütte (€10 for young DAV members).