you will rarely see a shark on a party boat. too many tangled lines. there are guys that fish for them. Fish On charters will charter a shark fishing trip also but i am not sure how good they are at it. typically all you will catch is b liners, squirrel fish, white snapper, a few red snapper the occasional grouper and a few kings by accident.
I have fished in Destin on party boats and charters for about 25 years now. There used to be some great party boats but they are all but gone now. The Emanuel, the florida girl, the lady eventheia were all greats.
The Destin fleet has became more of a tourist trap lately. there are still some great captains there but be careful who you go with. the biggest thing is do not walk up to any charter service and ask for any ole boat. The good capt stay booked by repeat customers so the charter services do all they can to try and get the not so good captains walk up business.