In this case a new artillery unit would just be an unnecessary complication. Light Cannons are already the “makeshift cannons” you describe since there are only a few rare instances of Iroquois using cannons. For both the Inca and Iroquois the circumstances were similar and the unit is already passable for both civs.
There’s also only a couple of other potential South American natives, Mapuche and Guaraní. And of those, Guaraní already has an option for a unique cannon, and Light Cannons would work just fine for Mapuche.
The best candidate for a new type of native cannon would be the Carronade featured in WoL. It could be a unit shared with civs such as Maoris, Hawaiians, and Haida since all used cannons captured from ships, and carronades are a style of naval cannon.