Every gun owner needs a .22 revolver and a handful of .22 shorts. I've never tried the quiet .22LR, but I guess they would work just as well.
Never thought about rabies and the bloodspray. I guess you should go with "trap and cap" outside or in a WMA like whacko said. I'm not safety conscious - I'd probably dump a 9 round cylinder into the thing and throw some bleach on the walls.
Carcass disposal is best done by cutting open it's belly to ensure some guts are coming out (wear gloves for crying out loud), swing twice around body and heave through liberal neighbor's window at 3:00AM.