How exposed to ideas from around the world would say, a trader or craftsman in say, Zanzibar, have been? How did these ideas shape the culture of East Africa?
Not sure about what is meant by European colonization - whether you are referring to European colonization in the New World (1400s) or the European colonization of Africa (also called the Scramble for Africa - late 1800s - early 1900s). I'll address the first definition, because clearly by the late 1800s I'd say a good chunk of African's were cognizant of the global situation to one degree or another.
To be fair, I pulled this from Eric Wolfe's "Europe and the People Without History," but his section on The World in 1400 gives a great macro-overview of the state of trade / communication networks in different regions of the world, and works to prove that "oriental" peoples such as those in Asia and Africa did in fact have a history prior to colonial encounters.
"Although Zanzibar may have been occupied by Arabs since the eighth century, the first port of major importance in East Africa appears to have been Kilwa, in control of the trade in gold from southern Rhodesia from the eleventh century on. Other important depots were Mogadishu, Kisimani Mafia, and Malindi. As the trade routes connecting Anatolia with the Persian Gulf and the Indian Ocean took precedence in the thirteenth century over the continental routes sponsored by the Mongols, the East African trade in gold, ivory, copper, and slaves increased heavily. East Africa thus became part of the trade network of the southern seas. In return for its exports, East Africa received Indian beads and cloth, as well as Chinese porcelain (mostly ming) and wares from Burma and Vietnam."
So, Wolfe points out that the peoples of East Africa at a minimum had contact with the Turks, and perhaps through them access to Asian goods from places such as India and China. Portuguese explorers (not necessarily colonists, remember) most likely also had contact with these peoples at the time, but I don't believe that East Africa established itself as the center of the slave trade in Africa until the early 1500s.
Source:
Eric R. Wolf, Europe and the People Without History, "The World in 1400," (Berkeley, CA: University of California Press, 1982), pg. 24-72