Jun 2, 2016 - 11:40 AM
Option 1 and 2 are the same hikes. Option 1 is down, option 2 is up. The Riffelsee is near the Rotenboden train stop. This area is currently still covered in snow, so I don't expect you can hike there mid June. Might be fine, but probably not. July to September is the best season for high elevation walks. The same applies to Blauherd.
Lower trails like Furi to Zermatt, and probably around Sunnegga and into the Zmutt valley will be fine. You can get the latest information from the tourist office. There will be plenty of options, but the highest trails will be inaccessible.