Depends on your weather conditions. Are you into nice warm sunny days with lots of flight, so they can go out to dump the garbage? If so, go for it. If no, put the frames in a freezer to wait for summer like days. The receiving colony also has to be strong.
As for illness from cleaning. Only a problem if it is illness that killed the colony. Always bee sure of what killed them before deploying the equipment to another colony. Else the new bees will just suffer the same fate.
Hope that helps