How much things would be different if the Mage had decided to hid Fluff in the Forgotten Box ?
Chat Blanc would have been the end of the world.
In terms of the main overall story, not too much would have changed, save for no Bunnyx, and Alix wielding another Miraculous and playing another role as a hero. Perhaps another Miraculous would have been placed in the Mother Box.
In terms of watching over the world and the flow of time, the biggest changes would have come from the role of other other Timekeeper kwamis. Those such as Intuition, Destiny, and Change would probably be keeping a much closer eye out on what dangerous events lie in the future; especially Destiny and Change. If actual time travel was needed the task would fall onto Apple, the Panda of Lineage; who would have to whisk a holder through time either to their ancestor or descendant to confront the threat they need to face. This would give Apple a very different role from the one he current plays, needing to focus on the world at large instead of on the individual like he does now.
For Chat Blanc in particular, it would have to be one of Adrien's ancestors or descendants sent to confront him and change the timeline, probably needing to seek out the Forgotten Box in order to revive all those that died with Vitaa. The world would carry on from the Chat Blanc timeline with identities being known instead of that event being changed.
Meanwhile in the Forgotten Box Fluff would be chilling, looking into the future to see how long it takes for Vitaa, Shii, and Uuince to finally get together, maybe betting on what future is most likely.