Nah, Stussy's stronger than that. Sanji has great CoO, he knows she isn't going to die from that.
Sanji focused on taking out Kaku because he trusted Zoro, who was apparently closer, to take care of Lucci.
I really wish people would give Sanji credit for taking out a serious threat like Kaku, rather than acting like he failed Stussy. Sanji has always preached doing what you can do, like what he told Usopp in Enies Lobby.
Sanji focused on taking out someone who could have easily hurt more people, including women like Nami and Robin, than reacting emotionally.
If Sanji hadn't restrained Kaku, what would have happened to Nami and Robin? Sanji was trying to protect his crew and the Punks, not ignore Stussy.