I just found out about a place in my area that teaches boxing, muay thai and mma. I am looking into taking boxing lessons.
My only concern is that these three styles require significant strength (including in the wrists) to be effective.
I have been studying wing chun Kung Fu for a while and it has actually helped me retain my mobility and fllexibility. It also doesnt rely on sheer srength to be effective. If punching with closed fists is painful for you, palm striking may work as an alternative.