I know the silence idea was mentioned, don't know about a pellet gun or a 22 rifle.
I would say that the quietest gun might be the 22 rifle and with earplugs and it has no kick. You remove two of the three scariest parts about shooting a gun and you have a chance.
Don't go to a range. The other guns will scare her. Find an outdoor private place to shoot.
If you can't get there, don't push it