I think it means that Corazon wouldn't kill his brother, no matter what he had done. If the positions had been reversed, and it was DD who was weakened and bleeding, Corazon still didn't have it in him to finish his brother off. Which is where Law is different from Corazon- Law is more than willing to kill DD. Which, as both him and DD have pointed out, makes Law more like DD than he would like.
His information scroll would've wiped out their entire family, so ya he would've killed DD and the family, thats one "trigger" that Corazon could've pulled to take down DD before Vergo intercepted him, and he definitelt would have pulled that trigger.
The other situation being when DD and his whole family had him surrounded and they both had a gun pointed at each other, he had zero viable triggers their, DD wouldn't die to him pulling that trigger.
It's confusing because the "trigger" Law insinuates about is something Corazon never had. He's speeking with the assumption that Corazon could've actually pulled something off, which still doesn't make much sense to say really, seems like a random tid bit he said to DD to shake him uo or w.e. it wasn't needed.