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

Here is Why You Need An Adapter

The outlet and plug type used in Swaziland is M and in New Zealand is I. This is how they look like.

New Zealand

In New Zealand, outlets of type I are in use.

Type I

Swaziland

In Swaziland, outlets of type M are in use.

Type M