How do you "cook" music with international flavor?

OK, I'm composing a horn quartet. The basic idea is a song repersenting Europe's imperialism by starting with a very pompus almost hymn-like theme, followed by a chaotic mess resembling a storm at sea (Both relatively completed). I then want to have a section that sounds Carribean and then another one to sound Asian to represent the colonies, ending by combining the theme at the begining with the two international ideas. Any suggestions to achieve these two styles without the use of percussion or special instruments?

There is no real need to use ethnic percussion. Sometimes that makes it worse, because you're taking the easy way out.

Learn about asian scales, like the dominant pentatonic, or the japanese scale.

Jamaican music is usually syncopated I-IV-I, if you want a bouncy calypso.

But since this is in the colonial age, just be creative. But you have no need for ethnic percussion. Trust me.