You Do Need power plug adapter while traveling from Switzerland to Isle of Man.

Here is Why You Need An Adapter

The outlet and plug type used in Isle of Man are C and G 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

Isle of Man

In Isle of Man, outlets of type C and G are in use.

Type C

Type G