The most impressive thing to me about how werewolves are used in fiction, is their ability to transform humans into other werewolves with their bites. Aside from the full moon myth, could it be potentially possible for an organism to 'infect' another organism and 'override' or 'corrupt' their physiology and essentially turn it into another? Are there instances of this happening in any way?
If you take a look at Rabies, you can already see a lot of parallels between the symptoms of it and vampire / werewolf mythology. There's an argument that this is the historical basis of some of the mythology in any event.
The problem with Rabies as the vector for transformation in this scenario is also its strength; it attacks the brain, causing massive changes in personality that are actually designed to spread the virus. While that's good for what you're proposing, it's also bad because it eventually kills the host.
But, for the sake of argument...
Imagine a modified rabies virus that still has the neurological damage but has a timer set on it; it only does neural damage for a specific period of time then stops, or lets the body's natural immune system overwhelm it, but only in the brain. In that scenario, you have a human or other animal changed (although not into a different species, just something barely recogniseable as human anymore) but is still capable of survival, albeit with the drive to bite and spread the virus according to the original programming.
This modified rabies virus, particularly if it starts introducing physical changes to a person after it abandons the brain, would give you all the appearance of a werewolf style disease, spread by bite, without genetic transformation.
Some living things have evolved ways to co-op other creatures and force them into doing their bidding. There are species of wasps that lays eggs into other creatures like spiders and caterpillars. These eggs hatch into larvae which not only eat their host from the inside out, but also infect the hosts brain and manipulate it. There is a fungus who spores can infect ants. Once infected, these ants are consumed by the fungus, and then are manipulated into relocating to a suitable spot for the fungus to leave the ant and continue growing. Parasites called hairworms can infect crickets. Once the hairworms infect the crickets they release chemicals that cause said crickets to move toward sources of light. This is done because hairworms need water to reproduce, and water reflects moonlight. The infected crickets haphazardly jump into bodies of water allowing the hairworms to emerge and reproduce.
P.S. There is an condition called Hypertrichosis that causes a werewolf like appearance.