When you chose a KK structure,

 4. Decide who the directors are to be. 

A Stock Company must have one or more directors.

It is not a requirement for directors to be Japanese nationals.

When you chose a GK structure, 

In a Limited Liability Company, each member executes the business of the company.

In cases where there are two or more members, it is determined by a majority of the members.

In cases where members who execute the business are provided for in the articles of incorporation, if there are two or more members who execute the business, the business of the company is determined by a majority of the members who execute the operations.