The cross is a symbol for Christianity. If you notice, Zoro and Mihawk have an east vs west theme. Zoro is the Eastern Samurai, wielding katanas, with attacks that derive from eastern faith and myths. Meanwhile, Mihawk is the European swordsman, wielding a large German Krieg messer, with gothic flavour and western religious paraphernalia. But, the cross is sometimes regarded as the symbol of the son of god. So that’s another way of spinning its significance on Mihawk.