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

Here is Why You Need An Adapter

The outlet and plug type used in Bahamas are A and B and in Swaziland is M. This is how they look like.

Swaziland

In Swaziland, outlets of type M are in use.

Type M

Bahamas

In Bahamas, outlets of type A and B are in use.

Type A

Type B