Indeed, pestilentia does seem to describe any contagious disease as well as actual plague, just like Italian pestilenza, Spanish pestilencia, and Old French pestilence. The Romans didn't think twice about pretty much reducing any epidemic to pestis, plague.
Actually I couldn't find any attestation of something like lebra est pestilentia, which would close ...
If you are looking for something to call these animals colloquially, I would go with the simple neuter opossum.
No other name will be easy to understand, and I value functional communication above sticking with classical words.
To in no way help me drive home this argument, here is a hendecasyllabic verse:
O, possum hoc animal vocare opossum.
Oh, I can ...
The adverb comminus should be considered. It literally means "hand-to-hand" or "at hand" and was used especially to describe close combat or contest. Cornelius Nepos:
comminus pugnans telis hostium interfectus est
which translated to English (J. C. Rolfe):
he was slain by the enemy's weapons in hand-to-hand-combat