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

Here is Why You Need An Adapter

The outlet and plug type used in Swaziland is M and in South Africa are C, M and N. This is how they look like.

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N

Swaziland

In Swaziland, outlets of type M are in use.

Type M