Didn't the wildlife officials realize that your dad put the poor animal out of its misery from a disease that would've killed it anyway? It's not like it would've lived the rest of its normal lifespan if he hadn't shot it. If it was showing symptoms it was already close to death! He did the right thing to protect you, other people, and to help the animal stop its suffering too.
I think you're right about white people having to be careful about how they react to blacks, but on the other hand, if your life is being threatened, I think anybody should fight back to defend themselves. It's best to avoid violence if at all possible. If you see a situation that could become violent, try to move away and if you can't move away, try to defuse it, not escalate it, but if someone is trying to kill you then you must fight back and you must do all you can to survive.