Lots of teachers already have concealed carry permits. Permissive concealed carry is the norm in the United States, with 40 of 50 states having either "shall issue" or "unrestricted" carry laws. They carry everywhere else, just let them carry at work, too.
Cops are over-rated in the handgun proficiency department. Most rarely shoot beyond whatever annual or semi-annual qualification is required by their agency. Anyone who competes in IDPA has more practice at "handgun combat" than the average cop.