Our school is in a similiar situation, but we have gone through numerous years now (knock,knock) without any arm injuries, we do long toss 2 days a week and players are required to do band work 3-4 days a week doing a version of the throwers ten excercises, we also go to the weightroom where players do light to medium weights, core excercises and on some days do the W,Y,T and I program. This has worked for us, some players have seen gains and some stay the same but we have had no one lose velocity and no one has had arm injuries, soreness has even been cutdown.
For your situational drills that we all do, even if arms aren't sore we do some walk throughs such as football, were the players go through the motions and try to use mind more than physical (it has worked for us) and fielding balls we have days where the players take fungoes galore but put ball in milk crate then run the crate in. But those are some things we do just to ease up on throwing, becuase no matter who you are you can't throw all the time.