Not many boats regularly targeting sharks any longer since you are not allowed to retain any Mako sharks and they are what most people want.
Having said that, check our sponsor charter boats here
https://www.njfishing.com/NJ_Fishing_Charter.php click on their links and look for boats that specialize in offshore fishing for Tuna. If you book the whole boat for a charter, I’m sure any one of them would be happy to take you out shark fishing but I doubt you’ll find any that will fish open boat for them.