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

Here is Why You Need An Adapter

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

Swaziland

In Swaziland, outlets of type M are in use.

Type M

Belize

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

Type A

Type B

Type G