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

Here is Why You Need An Adapter

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

Swaziland

In Swaziland, outlets of type M are in use.

Type M

South Africa

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

Type C

Type M

Type N