I'm not sure what the horrors of touching the flushing mechanism with your hand are. I'm pretty sure that the odds are in your favor that the previous occupant did not have leprosy.
And honestly, if the previous occupant had something icky on *their* hand when they used the flush mechanism, they're likely to have spread it to the door handle, sink, faucet handles (if not automatic), etc. You're not escaping any contamination.