How much is she realistically going to train? How much time is she going to spend dry firing? Is she going to attend any sort of decision based training with shoot/no-shoot scenarios? If the answers aren't "a lot, a lot, and yes" then I would shy away from anything with a thumb safety. The Sig P938 has a small and relatively stiff safety, and for that reason I would recommend against it for a new shooter, for someone who isn't going to be very dedicated to training and practice, and the cocked and locked carry can be intimidating to new users.
You need to be able to work the safety under stress, perhaps while being grappled, and you also need to leave the safety on right up until you decide you have to shoot or you've got a gun that has zero room for error with trigger discipline before an AD occurs. All of these are bad for the newbie or for the person who's only dabbling in firearms.
Guns I would look strongly at:
LCR revolver (Smallest, light, not much recoil, easy administrative handling to load, unload, clean, etc.)
M&P Shield (See previous post)
Sig P239 (A more expensive but "better" alternative to the Shield. Heavier, though, and slightly more complicated to work. I like the DA first trigger pull as a means of reducing the odds of an ND, but it is a bit harder to learn to shoot and you must religiously decock after firing but before holstering)
Glock 26 (a few more rounds than the Shield, easy gun to operate, but blockier and a bit tougher to conceal in most lady's clothing.
Changing grips doesn't effect the hand size to grip fit as much as you think. It' not the width that matters as much as the front to back length, sometimes called length of pull. Grip width effects concealment, but only marginally effects handling.