I had an idea:
Each day someone random will be killed.
The wolf does not know they are a wolf
so everyone thinks they are a normal villager.
eh, it's probably a stupid idea.
Go for it! Type up a rolesheet, too, if you wanna make it happen.
Here's a template.
Personal opinion: I'd give the wolf at least one indicator to make him distinguishable from the villagers. Like, normally wolves speak and behave differently because they're trying to hide their identity, but if the wolf doesn't
know he's a wolf, that's out the window. Something like "The wolf can only kill people he's voted for or have voted for him" or "Every villager role convo is an exact copy-paste, but the wolf's is slightly different" or something similar. Just so there's some logic and deduction going on alongside the wild guessing.