I trapped for many years and caught more than my share of skunks. I started out reading all the methods of killing a skunk so it didnt spray. Dont waist your time on reading things like shoot it so you break its back, use a long pole & snare to pick it up so its feet are off the ground, drown it (they cant spray in water) Thats BS, and the many hundreds of different methods! What I have found to be most reliable is just go ahead and kill it and they either will or will not spray. If you can kill it clean and quick from a distance before it gets excited your change is better it wont spray. However I have seen them spray with their last dieing reflex.
For disposal put them in the burn barrel with a lot of cardboard or fast burning wood. The smoke will smell a little for a while but it wont hang around for days. They burn almost completely because of the large amount of fat in them and the spray its self is more flammable than gasoline. Dont smoke while your killing a skunk cause if it sprays it will ignite with the prettiest blue flame youve seen!
Be there done that and it works sometimes and some times not!