You Do Need power plug adapter while traveling from Palau to Switzerland.

Here is Why You Need An Adapter

The outlet and plug type used in Switzerland are C and J and in Palau are A and B. This is how they look like.

Palau

In Palau, outlets of type A and B are in use.

Type A

Type B

Switzerland

In Switzerland, outlets of type C and J are in use.

Type C

Type J