No, Zoro doesn't have to fight every character that uses a sword, he could just go for the strongest sword user and defeat him thereby becoming the WSS.
There is a possibility that Mihawk thinks Shanks is stronger than Big Mom and just decided she wasn't worth the challenge.
Like I said, Big Mom rarely uses Napoleon cos everyone bar high and top tiers are worth the hassle.
Luffy????He can't even use simple air slashes loool, he is disqualified.