Ebola and smallpox seem to have pretty similar transmission, expressing in aerosols and bodily fluids, direct contact, contaminated objects, but also conventionally limited transmission (distance, infectivity window, etc.) Did corpses remain infective, were there special protocols for handling them?
For bonus points, did smallpox virus persist in semen after recovery?
As long as it is protected from the outside environment the virus can remain infectious. So until the host is significantly decayed, many viruses could be present.
Most viruses "die" within a few minutes outside of the host. If they are in warm water droplets they could survive for longer. But with smallpox infectivity wanes in 7 to 10 days when scabs form over the lesions, but the infected person is contagious until the last smallpox scab falls off.
I'm no scientist, but from this I'm going to guess that as soon as the skin and flesh has rotted to a point where no lesions are accessible then it would be no longer infectious.
The smallpox virus is most spread by the act of breathing and spreading from the water droplets that we give off from it, but can be passed by other bodily fluids. But these need to relatively warm or the virus dies. The virus was still dangerous until the affected area either healed, rotted, or was removed completely (burning of corpses and used sheeting).