I know that you mentioned getting away from traditional Olympic disciplines like air rifle and air pistol. I think that would be a mistake, particularly if going to be a true "school" team, and not just a youth shooting club. The air disciplines (10m air rifle and pistol) are college scholarship sports and Olympic events that the students can engage year round. The school needs no extra facilities, and any space that can be opened up to 10 m and doesn't have cross traffic can be used. It is a very good "starter" shooting sport for schools, particularly in areas where there isn't an established shooting culture. Putting little lead pellets (or lead free if that's an issue) through a round circular bullseye, with a very quiet air gun, is a very good way to begin to get people to move away from preconceived notions of firearms. Yes it is a vastly different from how most of us enjoy shooting and competing, but it teaches extremely solid fundamentals that transfer to any other discipline with firearms. Small bore would be the logical follow on from there, particularly if you get community buy in (sending a kiddo to the Junior Olympics for instance), though it now moves into needing a real range, lead control issues, etc.
-Jenrick