Concerns about Westies and Rat-Diseases

Question
Hi, my Westie is the prime of his species; this one is a natural ratter. He was given to us by a family member who carelessly picked him up from a shelter without knowing very much about his breed, but we had dogs already so we knew how to care for dogs in general. It didn't take long to find out we'd ended up with a purebred Westie simply by his appearance and energy levels alone. However, being generally ignorant of the West Highland Terrier's breed instincts towards vermin, you can only imagine our surprise when we found our little adopted one in the process of a kill, snapping the neck of a rat the size of our chihuahua. With little research, we found out about the rat-killing instincts and brushed it off.

However, the number of rats in our neighborhood has been increasing lately and, within the same 24-hours, he killed two rats and chased away a third. He doesn't eat the corpses (merely snaps them dead and then leaves the remains for us to clean up), but we're still concerned about possible diseases he might catch from his rat-hunting. He's up-to-date on all his shots and (to date) hasn't been bitten back by the vermin he kills. We know we won't be able to train the instinct to kill out of him and these rats don't seem to be getting any less of a problem. We have traps and devices to drive them off our property already, but this is a rodent-war that's far from over. Are there any medications or any precautions we can take after each future kill to keep him healthy and disease-free?

Answer
I think it's great you have this dog and very lucky considering the circumstance. He must feel so proud of himself too. I think you appreciate the natural order of what this dog is doing. An interesting read on the subject is
Terrierman.com
I believe the dog is fairly safe as long as there is no ingesting of the rodentl but leptospirosis is a problem to be wary of whenever there are rats. Be careful the dog does not drink from puddles especially where you know the rats are out doors
They really just go for the neck snap as you say and the more they hunt the more adept at that they become.
One other thing to be careful of is a rat that has ingested poison should your dog break skin and swallow contaminated blood
I would  def have a treatment handy so speak to your vet about what you should do in case of an accidental poisoning. Make sure to get rid of the dead rats immediately.
Good luck - hope this was helpful