One could really think that Shanks (therefore Mihawk as well, like it or not) is confirmed stronger than Kaido, let alone Big Mom
Green Bull is confident that he can fight and take out Luffy, who just defeated Kaido
And possibly face the intere Alliance, with other strong people like Zoro, Law, Kidd, Yamato etc which he perfectly knows they are there
But he shits on himself at the mere idea of having to fight Shanks...