Traditional Zulu society seems to have been largely secular, in that there isn't something like an overarching religion. Traditional Zulu society did prominently include a number of beliefs in what from our perspective would be supernatural (if you include drawing magical powers from natural phenomena as supernatural), which still has some currency among many Zulu. There was widespread use of divination (by diviners called isangoma (singular) / izangoma (plural) ) to discover the cause of anything unusual. There was the belief that the order of nature could be manipulated for ill by sorcerers (umthakathi / abathakathi), who were capable of putting people into a position of deep vulnerability (isifo), something like being cursed. More generally, many parts of the natural world has powers (umuthi) that can be drawn from and used for good or ill by herbalists (inyanga / izinyanga). Finally, and closest to something recognisable as a religion, there was the belief that ancestor spirits (idlozi / amadlozi) could see to the protection and well-being of a family, or if aggrieved punish them with misfortunate. This is often referred to as ancestor worship, and the ancestors feature prominently in Zulu social practices with lots of rituals and occasional sacrifices directed towards them, but by most estimations the belief that the ancestors can influence the world is just one element in a wider range of supernatural influences, as I hope to have indicated.
By the time of Shaka there was already Christian missionary contact by way of the European colonies to their south. The really large missionary push came however only came with Shaka's successor, Dingaan, who invited missionaries to come to the Zulu. It's not impossible that there was some distant contact with Islam, by way of the east African trading networks that the Zulu had some links with, but it doesn't seem to have had any influence (Islam extended as far south as what is now northern Mozambique, which is still decently far away from Zululand).
Historically there has been some claims that the Zulu have something like a creator god who orders nature but doesn't interfere with human affairs, often called 'unKulunkulu' (the very old one). Most of what I've read reports that this is probably the product of attempts by Christian missionaries to introduce the notion of a godhead to the Zulu as part of their attempts to convert them. While Zulu will nowadays generally affirm the existence of unKulunkulu, Zulu nowadays are overwhelmingly Christian or participate in a native church that mixes Christianity and traditional beliefs. There is no firm evidence of this belief being present when the first traders and missionaries arrived; in contrast, many missionaries seem to have despaired at how any recognition of a godhead had departed from the Zulu (a survey of these reports is in the article Lord of the Sky-King of the Earth: Zulu traditional religion and belief in the sky god). So, there is no good evidence this was around in the time of Shaka, and decent evidence that it wasn't.
There are also mythological figures like 'uMvelingqangi' (the first ariser), a male figure who was the first animal to arise (out of a pre-existing natural world), before humans, or uNomkhubulwano (she who chose the state of an animal), a female figure who oversees the rains and brings fertility. They clearly are part of the Zulu cosmology, along with a large range of other such figures. But despite the import of cosmology on traditional Zulu practices (for instance, providing a framework for indicating which parts of the natural world has what powers), there isn't any indication that this amounts to a religion. For instance, Zulu rituals and ceremonies revolve around the household, without there being anything by way of temples or a priesthood for these cosmological figures.
Sources
Body and Mind in Zulu Medicine - Harriet Ngubane
'Lord of the Sky-King of the Earth: Zulu traditional religion and belief in the sky god' - Irving Hexham
Zulu Thought-Patterns and Symbolism - Axel-Ivar Berglund