Sounds like you've got a good handle on the direction you want to head. The first question I would ask is, do the class rooms already have first aid kits in them? First aid kits and first aid training for staff would be my first concern. Its far more likely a student will be injured in an accident in the classroom then a major emergency will occur. Plus that gives you a strong base to build from, I think every teacher will easily see the need for basic first aid. And its an easy expense to justify.
Then you can ramp things up. We all know mental preparedness is key number one, if the staff aren't used to thinking in a survival mindset you'll have to ease them into it. Jumping in too hard and fast my engender a lot of resistance.
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A gentleman should always be able to break his fast in the manner of a gentleman where so ever he may find himself.--Good Omens