Not a Catholic, but historically I thought the Knights Templar wore black crosses on their shields and cloaks.
No, the Templars wore a red cross, indicative of their origin as a military order and combat force that would see its own blood spilled, if necessary for victory.
Teutonic Knights were the ones that often had black crosses. Templars were red. Hospitallers were white.
There were a bunch of others but I think those were the bigh 3 and tended to have the simpler cross designs...been a bit.