If we see the list of Shichibukai, almost all of them have some reason to become Shichibukai.
Boa Hancock became shichibukai to protect Amazon Lily from marine. Gekko Morai, Doflamingo, Crocodile etc had their black work or evil deeds, which needed to be protected from marine.
But I don't remember anything about the Mihawk. He is alone but strong, so he don't need to fear from marine.
What is his real intention to become warlord?