Presumably, if not himself, then one of his male Habsburg cousins. FF may even give it to his oldest son given that they could not inherit the (A-H) Habsburg throne. There's no way its going to an outside party and risking the chance it leaves the Austrian orbit.
In fact, an independent Bosnia with an independent king will inevitably resort to the protection of Austria because Serbia Karadovic have plans on Bosnia and this means an existential threat to Bosnia, which forces the Bosnian king to Austrian protection
Therefore, I have no fear of their exit from Austria's influence as long as Serbia threatens them to a great extent
I think that the King of Bosnia will follow the pattern of his choice, similar to Albania
(A Protestant European nobleman or happened to have the lineage of the ancient kings of Bosnia and does not belong to one of the religions or races of the Bosnian state, and most importantly, he has distinguished relations with other European families)
This effectively excludes the Habsburgs, the Savoy, the Ottoman dynasty, Muhammad Ali, the Romanovs, and any orthodox royal house from the nomination for the Bosnian throne.
So candidates like Prince Waldemar of Denmark (the only son of Christian IX who never became king) or Prince Wilhelm, Duke of Södermanland would be ideal.
(Valdemar is better because with the situation of Bosnia so threatened, its relations with the great powers will be very important for Bosnia)
But regardless of the candidate, how do you think Bosnia will develop?