Rabbits are what a .410 was created for. I use 2 1/2" 4s since one 4 anywhere important will kill a cottontail just fine and it leaves a very visible track in the critter so you can find and extract it before cooking. And there are just enough 4s to kill 'em and not pepper 'em. I suspect that most rabbit .410s are full choke and their patterns with 4s are patchy but lethal. You do have to be careful not to shoot the hounds or the houndsmen, but I still think it's safer than quail, who tend to fly between hunters. A little restraint is called for, that's all....
I also like to shoot cottontails on cold mornings with an air rifle or .22 with CB Longs.
No reason to carry them around uncleaned; it takes about 10 seconds to clean one and pop the skint and gutted carcass into a plastic bag. You need to carry a heavy knife or a really sharp hatchet to whop the heads and feet off, tho. Very tasty; the "schmoo" of the uplands.
I was raised on a cattle ranch and spend time in the so-called third world each year. Smellproof. (There are MUCH worse smells in this world than rabbit guts. Think Haiti.).