If he's not the leader, then he wouldn't be seen much differently. Look at Zoro and Sanji, for instance, they're not even worth as much as the people they defeated because of Luffy's deflated bounty. So a captain would have more of an impact on the underlying than the other way around. Meanwhile, Mihawk doesn't have a captain that is a bigger threat than him for his bounty to receive inflation. Moreover, Mihawk already has a reputation as a marine hunter, so nothing really changed about him as far as threat level goes.