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

Here is Why You Need An Adapter

The outlet and plug type used in British Virgin Islands are A and B 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

British Virgin Islands

In British Virgin Islands, outlets of type A and B are in use.

Type A

Type B