You Do Need power plug adapter while traveling from Saint Kitts and Nevis to Swaziland.

Here is Why You Need An Adapter

The outlet and plug type used in Swaziland is M and in Saint Kitts and Nevis are D and G. This is how they look like.

Saint Kitts and Nevis

In Saint Kitts and Nevis, outlets of type D and G are in use.

Type D

Type G

Swaziland

In Swaziland, outlets of type M are in use.

Type M