You can certainly walk from village to village on your own, and the website gives some good suggestions. However, in early May you will be severaly limited as to routes in the BO and Valais. The multi-day walks they suggest in the BO, for example, include the Alpine Pass Route, which is impassible in May due to high passes. Even the lower elevation route they suggest, the Berner Voralpenweg, which traverses the lower Voralpen from Gstaad to Spiez, climbes over 2 passes over 2000 meters---very likely still snow-covered and hazardous in early May.
Same with the Valais. The lovely Aletsch Panoramaweg from Blatten to Fiescheralp starts at 2100 meters and climbs up to 2550 m---that's over 7000 feet.
The only multi-day route I saw that would work in May is the vineyard walk in the Valaiss, from Martigny to Leuk. This stays under 1000 meters the whole way---but the route just follows above the road in that area.
If you truly want to do this in May, you need to look at lower-elevation areas in other cantons---maybe Appenzell? I'm not familiar with that area so I can't make any suggestions. In central Switzerland, there is a "Weg der Schweitz" theme path on Swiss history along the Vierwaldstattersee (Lake Lucerne) but I don't know how interesting it would be.