There’s zero reason for Mihawk to ever join Blackbeard, and thus the whole idea falls apart. BB can’t give him what him wants, which is for his chosen rival (Zoro) to challenge him in an epic duel for his title. Mihawk has worked alone since Roger’s execution, there’s no in-story reason for him to want to change that, and if he kidnaps Perona while she’s looking for Moria, this is more likely to make an enemy out of Hawk-Eyes than anything else.
Given Hancock’s hatred of all men and Luffy’s status as the fifth emperor, there’s no reason for her to team up with BB over Luffy. To do so would be completely out of character for her.