Short hairstyles for black women over 50? No troubles with that. There are plenty different styles that would suit women over 50. It is well-known that hairs of African women are mostly thick and there exist plenty of short styles, which would perfectly suit them.
Age is not a verdict and there are such beautiful ways to cut hair that aged women would reappear in a novel light. Selecting a proper style will not make look comic and incongruously.
Conversely, you will be enchanting and fabulous. And no one would heed to your age, as you will be renewed and young again. No time for hesitations. Select the proper style and shine!