We know that the Imperius curse works against non-human animals as well as humans, so it should work on transfigured humans. A werewolf could probably be considered a transfigured human so it should work on them.
If so, why not use the Imperius curse to keep them in check?
Is it just because using the Imperius curse on a human can earn you a life sentence in Azkaban? Isn’t it still better than killing somebody? If both, the possible victim and the werewolf, for example, someone like Lupin) is willing to the idea, is the only reason stopping an arrangement like this from happening is a legal technicality?
In Prisoner of Azkaban, Lupin would never have been hired without Dumbledore, so Dumbledore was already willing to take risks. If Dumbledore would do it himself without bringing in the authorities no one would even know about it. We also know that it is possible for a powerful enough wizard to cast an Imperius curse on someone then just leave them alone to go about their daily life, in such a way that they will till be subservient to the caster. Why wouldn't Dumbledore do something like this with Lupin (just for the duration of his transformation, since Lupin would probably consent to it as well)?
We know that forgetting to drink the potion didn't turn out well for Lupin. If an arrangement like this had been made since the beginning, they would never have had to worry about not being able to drink the potion. Also it might be easier to keep the werewolves in the wild in check this way, which is still better than killing them (if imperious curse on a werewolf is illegal because it is technically being done on a human being, then killing a werewolf should also be illegal since it technically still a human being.
So why isn't this done with werewolves?