I wouldn't disinfect the container with the other cats- if they've already stopped eating, they can't get the virus. It can only infect them orally (assuming your cats aren't needle-using drug addicts
For handling, it's ok to move the cats that are wandering around looking for a place to hang, but once they J-hook, they're very delicate and shouldn't be moved. Once the chrysalis has hardened, it is possible to move them but they are still easy to drop and damage.
good luck! -Scott
(ps I try to bring in eggs and hatchlings, mainly. That reduces the chances of parasitism and disease. Some people rinse the milkweed leaves before giving them to the cats, but I don't normally do that)