THEY. DON'T. NEED. TO. FIGHT. CROSS. GUILD.
Only Mihawk matters, and he can do whatever he wants, so can Zoro. If Zoro wants to come to his doorstep and have a duel with him, then so be it.
The rest of the Straw Hats don't need to care or get involved in that, it's Zoro's fight and Zoro's fight alone.