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

Here is Why You Need An Adapter

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

Switzerland

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

Type C

Type J

Belize

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

Type A

Type B

Type G