Whatever the plane is registered, that is the license that you will need.

I was flying a plane registered in Sao Tome, so I had to get a Sao Tome license. Then, the registration was switched to Kenya, so I had to get a Kenya license. The company was planning on get a new plane, with a Bulgarian registration, to fly in France, and they told me they would be getting me a Bulgarian license if it came to fruition.

In most places, to legally fly in a plane registered in their country, you need only take an "Air Law" test, which covers the legal differences in their country, and is normally 40 questions, and is not too difficult. In Japan, you also need to take a Radio License Test. Kenya was different....we had to take a "License Conversion" test which was 100 questions and covered ALL of the JAA 24? subject areas.