You Do Need power plug adapter while traveling from Solomon Islands to Tokelau.

Here is Why You Need An Adapter

The outlet and plug type used in Tokelau is I and in Solomon Islands are G and I. This is how they look like.

Solomon Islands

In Solomon Islands, outlets of type G and I are in use.

Type G

Type I

Tokelau

In Tokelau, outlets of type I are in use.

Type I