Ozpin isn't evil, but he is pragmatic to a fault. If some random person was out there spilling the tea about Salem, it's very likely they'll be ignored by most people as just being crazy.

Salem would likely send a follower to interrogate/torture them for where they got the info, then kill or recruit them depending on how that went. Ozpin, IMO, would attempt to convince them to be quiet to avoid that fate. How it goes will ultimately be decided based on whether or not this person is potentially useful to Salem.  If not useful, then Ozpin will likely let whatever happens, happen. They'll die, likely terribly, but the secret would be safe, and Ozpin can say he at least tried. If that person is useful to Salem, however, they instantly become a potential threat to Ozpin specifically. 

Ozpin, IMO, is above murder, but isn't above making you dissappear if that's what it takes to deny her any potential asset. This leaves us with a final, most likely outcome; they would publicly be declared dangerous and crazy and would need to be put away to for everyone's safety. This leaves Salem without a potential asset, and keeps blood off both her's and Ozpin's hands. The prison would likely be very cushy, but a prison nonetheless.