I flew over 2 dogs, 2 giant african land snails, 1 corn snake and 1 goldfish (!) back in July.
BVET - as referenced above - are your best bet for requirement information.

It was not a hassle paperwise - you need an import permit. Once you've filled in the form they will issue it immediately via email.
BVET staff speak perfect English and are very prompt in replying to requests for information. They also have much of the information in English on the website.

I would recommend you use a proper carrier service that will deliver the animals to your door once in Switzerland to avoid any stresses with being kept in kennels etc.

Our carriers kept the snake, fish and snails on their offic desks to keep an eye on them for the few days before they flew out.

As far as I am aware you will not be allowed to take any of your animals in the cabin.

Sx