You Do Need power plug adapter while traveling from Switzerland to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Switzerland are C and J. This is how they look like.

Switzerland

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

Type C

Type J

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K