I sure hope they don't allow the hostages to be in-laws. I think they would get hit much more often than the hostage takers!
Using a shotgun to pick hostiles off of friendlies is not good idea. An assault rifle would be way better. I would even prefer to use a handgun for such "surgical" work. Now if that was a rifled barrel shotgun with slugs and a scope, that might work too! I'd just be a bit concerned about over penetration.