Has she tried wearing some sort of hearing protection?
You could try 22 CB caps or BB caps. They are intended more for indoor target shooting so the range on squirrels would be really limited.
.22 BB Cap
.22 Bulleted Breech Cap, is a .22 caliber rimfire cartridge, .22 BB cap and .22 CB refer to cartridges that are low velocity and project reduced noise. These rimfires closely resemble a .22 caliber air rifle in power and are often used for indoor shooting and close range pest control. Developed for indoor shooting galleries with special "rimfire gallery guns", the .22 BB Cap was the first rimfire cartridge, dating back to 1845. It has no separate propellant charge, relying on the impulse created by the primer alone to fire a round lead ball.
Specifications:
Case Length: 0.284 in.
Overall Length: .343 in.
Bullet weight - 18 gr. / Velocity - 700 fps. / Energy - 20 ft.lb.
.22 CB Cap
.22 Conical Ball Cap, is a .22 caliber rimfire cartridge which has a very small propellant charge (usually no gunpowder, just the primer), resulting in low muzzle velocity. This is similar to the muzzle velocity produced by a low to mid-power .22 pellet gun, however it should be noted that the bullet from a .22 CB cartridge is significantly heavier than a typical airgun pellet and therefore carries more energy. Due to their low power, CB rounds can be trapped by most pellet gun traps. CB rimfire rounds are often used for indoor shooting practice or for small pest control in areas where a limited range is an advantage due to crowding. The original .22 CB rimfire cartridge has the same case as the .22 BB Cap.
Specifications:
Case length: .284 in.
Bullet weight - 20 gr. / Velocity - 700 fps. / Energy - 22 ft.lb.
Bullet weight - 29 gr. / Velocity - 350 fps. / Energy - 8 ft.lb.
