I would recomment checking out some of the Keen brand of shoes. While the offer a great sandal as well, I call the 4-Wheel Drive Sandals, because they are great for dry hiking, I am not sure they would be the best in Switzerland. However, they make some great shoes that are comfortable for all around travel. They look good enough that they can be dressed up for an evening out after they have spent the day hiking up and down a mountain. They make a variety of styles, some with beefier treads than others. Leather uppers with a good lug sole should allow you to get by without taking multiple pairs of shoes. Although they may not work with a skirt or dress.
If you want sandals for Italy, make those what you wear on the plane. The easy on easy off aspect of them makes security a breeze.
For any walking and hiking, do not underestimate the value of good socks. Hiking socks by Thorlo or Bridgedale (the Ventum model is great) give comfort and dryness for full day of hiking.