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

Here is Why You Need An Adapter

The outlet and plug type used in Turkmenistan are C and F and in Swaziland is M. This is how they look like.

Swaziland

In Swaziland, outlets of type M are in use.

Type M

Turkmenistan

In Turkmenistan, outlets of type C and F are in use.

Type C

Type F