Check your local hunting regs closly, and esp' the local Animal cruelty mandates.
Often even while Feral the Cats are governed under laws for Domestics, and have to be handled as such.
Also shooting stuff that you are not hunting gets you the title of SLOB hunter, and gives the Antis fuel.
Besides which Cats spreading Rabies is a myth that goes back to the middle ages.
Clinical research has shown that Rabies in Domestic cats has a very short shelf life..ie the animal drops dead very very quickly of said disease, and they are not social animals with there own kind, and take great pains to avoid each other unless it is mating season.
Where as Coons survive Rabies allot longer, and often live in social groups (to a point), which can spread Rabies further.
Out here in BC in 10 years of dealing with Feral Cats in and out of shelters, and vet clinics I have never seen a case of rabies in Cats. Best to leave them be...they sort themselves out.