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

Here is Why You Need An Adapter

The outlet and plug type used in American Samoa are A, B, F and I and in Swaziland is M. This is how they look like.

Swaziland

In Swaziland, outlets of type M are in use.

Type M

American Samoa

In American Samoa, outlets of type A, B, F and I are in use.

Type A

Type B

Type F

Type I