What arms market created the Soviet-Chinese border wars?
The war between Communist China and Communist Vietnam?
The war between Communist Vietnam and Communist Cambodia?
The Rwandan genocide?
World War II? (The allies were disarming, and the Nazis were making their own)
War existed long before international arms markets. It has always existed and will always exist. Some of the worst wars were fought long before any significant international market in arms existed.
Consider the Mongol conquests of the 1400s.
Tribal peoples were almost always at war, and almost always working on ways to wipe out their neighbors.