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

Here is Why You Need An Adapter

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

Swaziland

In Swaziland, outlets of type M are in use.

Type M

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I