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

Here is Why You Need An Adapter

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

Tokelau

In Tokelau, outlets of type I are in use.

Type I

Solomon Islands

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

Type G

Type I