Relative to the U.S., the mountains in Switzerland are not that high. I would talk to the baby's doctor. When we've traveled to high altitudes (Hawaii, Switzerland, Colorado, etc.) the key is to not jump off the plane and then proceed to the top of some peak. I think if you would get to a city, Wengen, for example, spend the day at that altitude and the next day go up to higher altitude.
Does your baby seem adaptable to changes in routine? That might make a difference. We took our 4 kids everywhere from about 3 months on. They became good little travelers. One of my sons and his wife have traveled with their now 2.5 year old a lot. He is a good little traveler, but of course, he's a little guy, so he needs to be accommodated, somewhat. They pick up food at Target so they always have something he'll eat. And, when they went to Hawaii from Minnesota, he was getting up at about 5 am. That, I feel is to be expected. At home, he has a fairly strict routine. But, while sightseeing in Hawaii, he just would nap when necessary whether it was on a hike or in a car. My other son has not traveled as much with their child and now when he does travel its more difficult. Obviously, there's differences in children.
Six months is a fairly nice age to travel with a baby. A toddler is more difficult on a plane. I would have had a hard time leaving a baby for 10 days, but everyone is different.
If your baby is breast fed, that would make it all super simple. If not, my grandsons' parents have a thermos type thing that heats up bottles. If possible, you might wait to start solid foods until after your trip. Again, talk to the doctor. If you need advice on front pack carriers or car seats or strollers, etc. let me know. I would advise bring OTC meds like tylenol and motrin, and know the dosages, again, talk to dr.