You Do Need power plug adapter while traveling from Liechtenstein to Cocos (Keeling) Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cocos (Keeling) Islands is I and in Liechtenstein are C and J. This is how they look like.

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I