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

Here is Why You Need An Adapter

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

Cocos (Keeling) Islands

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

Type I

Liechtenstein

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

Type C

Type J