IMO many martial arts would suit your needs provided you find the right school and teacher. For conditioning, strength and balance building you merely need to practice in a no or light contact situation and many schools can accommodate that.
Chi-gung exercises (qi gong) are done by Tai-chi-Chuan practitioners to get their bodies in shape for the fighting aspects. Some chi-gung is slow, but others are not. Here is a link to a type of chi-gung called "animal exercises" (now referred to as "zookinesis"):
Rather than a specific art, I would recommend you find an instructor who is willing and experienced enough to work around your limitations. I know they are out there. Our school does this with folks who have all kinds of handicaps. I know of another Wing Chung school that does also. We are in Delaware USA, The other is in New Jersey USA.
I am aware of Tai Chi. Are there other martial arts I should consider? I am looking for exercise that will help core strength and balance. I was in a motor vehicle accident a few years ago and suffered a mild brain injury from which I fully recovered; but, I need to avoid sports with risk for blows to the head. The accident also left my wrists fragile, although I'm about to have surgery to get a partial fusion on my right one.
I have always been interested in martial arts but over the years chose other forms of exercise. I'm buddhist and have been meditating on and off for a few years and just feel that now seems to be the time to begin a martial art that will help me improve my core strength/balance and help with daily stresses, etc. I tried a 6 week tai chi course and I'm sure over time I would get great benefit from it but it seemed a bit slow and I just wonder if there are other options out there.
Thank you.