Hand orientated fighting styles?

Depending on how bad the leg is, it would still be hard to strike with the hands. Power in punches and other arm strikes comes from a strong stance and footwork. The best boxers are the guys with the best footwork, in many cases.

Boxing, Wing Chun Kung Fu, Xingi Quan, Hung Gar Kung Fu, certain karate systems (Goju-Ryu, Isshin-Ryu, and Uechi-Ryu come to mind), and certain Silat systems (Harimau, I think, for instance) focus more on hand strikes than athletic kicking. Some grappling systems are designed to throw and lock an opponent while maintaining an upright position- Hapkido, Aikido, and certain Jujitsu systems fall into this category, and many of the movements and strategies can keep the leg from having a lot of stress placed on it. Certain military combatives systems, like those used by Fairbairn during WWII, don't require a lot of athletic movement, and the only leg strikes thrown are kicks to the knees/shins and knee strikes to the groin.

If this is just a one-off scene, just about any martial art should give her some basic tools that don't involve her having to kick or place a lot of weight on one leg if she doesn't want to. If defending herself against attacks is a regular part of her life, carrying a weapon, like a stick or knife, might be a better idea. A stick in particular can give her some extra range on her attacks, which would help keep the attacker away from her leg; a collapsible baton fills in for a stick quite nicely. The Filipino martial arts of Escrima, Kali, and Arnis specialize in using short sticks.

If I had a better idea of her physical limitations, I could offer more specific advice. In the short term, if she wants to keep her leg away from the opponent to avoid injury, she'll place it behind her and put a lot of weight on the front leg.

You can adapt practically anything you can learn to meet your need. If you are in a sport it may have rules like you have to do so many kicks. but n self defense the use of the legs or feet is your choice as the martial artist. If the person can't stand it would create some challenges, but still not impossible. There are people training in wheelchairs or people with cerebral palsy.

Martial arts are not hand styles. Only in the sports arena are they thought of as separate thing like stand up, grappling, etc. The truth is most traditional arts incorporate all aspects of training with strikes, joint locks, throws, chokes, traps, pressure points, etc.

There are numerous styles she could use, any styles within the Karate of Kung fu divisions, but without having a grasp on whatever the style, your story won't be very believable. I'd stick with boxing, maybe research a few hand strike names but don't get too carried away with the descriptions. Depending on the type story, you might be better off giving her some kind of technological brace, maybe with throwing knives hidden into the brace, or some sort of bionic like function that actually enhances the leg, rather than a limitation. Make her limp or however you describe the "bad" a ruse.