You can go to a shipping company and rent a container, they cost around 1000 to 2000 CHF. You would have to pack your own stuff and take it to the place where the shipping company has the container. I have done it this way and saved around 5K. Just go and talk to the shipping company directly tell them you want to rent a container and send it to Israel.
Was it a Swiss or Israelian firm that came up with that price? Normally it's cheaper to have it done by a mover located in the country of destination, than when using a Swiss one.