This is an area of historical research that has been very active in the last 15 years or so. Among the notable books on this general subject:

Storey, William Kelleher. Guns, Race, and Power in Colonial South Africa . Cambridge ;: Cambridge University Press, 2008.

Macola, Giacomo. The Gun in Central Africa: A History of Technology and Politics. Athens, OH: Ohio University Press, 2016.

Aderinto, Saheed. Guns and Society in Colonial Nigeria Firearms, Culture, and Public Order . Bloomington, Indiana: Indiana University Press, 2018.

These historians have added a lot of nuance to previous histories of guns in sub-Saharan Africa, but the baseline picture is somewhat as the OP imagines.

Guns came into West and Central Africa as trade items during the rise of the Atlantic trade. It's long been argued that guns played a meaningful role in intensifying conflict and fueling more active slave-raiding by some coastal polities. That still seems to be true, but Macola's 2016 book argues strenuously that the picture is more complicated in several respects.

Macola pointedly observes that different Central African states and societies incorporated guns obtained through trade in very different ways, and that many of them that had access to guns and owned them did not use them extensively in military activity but instead reworked guns as prestige possessions and art objects, restricted their ownership to elites or royal households, or used them only in specific military contexts (in the case of the Yeke state, in ivory hunting and slave raiding). Macola's point, I think, is one that Storey raises as well (though Macola criticizes Storey for being too focused on the perspective white settlers in South Africa, and yet I think Macola's evidence drawn from other sources is pretty thin)--that it's important not to view guns in sub-Saharan Africa through the lens of technological determinism, that Africans had considerable agency in their acquisition of and use of guns (or refusal to do so). Macola and Storey also argue that most African elites were keenly aware that extensive military reliance of guns would place them in a position of dangerous dependency on importation--not just of the guns themselves but also gunpowder.

There's a good deal of evidence in other historical research not primarily focused on guns for this last point--West African rulers from a very early date sought to acquire more information about gun and gunpowder production, and blacksmiths and artisans across sub-Saharan Africa developed considerable practical know-how about the maintenance, modification and repair of the guns they had (which in time spanned guns ranging from the earliest flintlocks to mid-19th Century rifles). Macola argues that even into the colonial era, there were groups in south-Central Africa that engaged in gunrunning or in illicit acquisition and modification of guns despite colonial restrictions on African gun ownership.

That last point is also the major focus of Aderinto and Storey's histories--how gun ownership became intertwined with white supremacy and imperial power. This is a primary interest of all Africanist scholars writing on this general subject: to show both that Africans in different parts of the continent were conversant with guns, thoughtfully selective about their usage, aware of the vulnerabilities of dependence on importation, etc. before the imposition of European imperial power in the late 19th Century, and that imperial ideology that guns were a new and dangerous introduction into African life and had to be controlled as a result was racist nonsense. Aderinto gives a detailed account of the precise use of guns and gun rights in colonial Nigeria to symbolize and structure racial hierarchy--'ordinary' Nigerians were only allowed to own old-fashioned muzzle-loaders, 'educated' Africans were allowed shotguns, and only Europeans and military or police directly under their command were allowed more powerful firearms. This was both a way to structure and communicate racial and cultural hierarchy and not coincidentally also to suppress any possibility of armed rebellion against European rule.

That leads also to the subject of guns in postcolonial Africa, which is a pretty sprawling and complicated issue in its own right, but this is already a long answer.