You Do Need power plug adapter while traveling from Wales to Liechtenstein.

Here is Why You Need An Adapter

The outlet and plug type used in Liechtenstein are C and J and in Wales is G. This is how they look like.

Wales

In Wales, outlets of type G are in use.

Type G

Liechtenstein

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

Type C

Type J