Regarding the rules
We have discussed firearm regulations for fishing on this board a few times over the last year or so - just do a search. I contacted the State Police about it and got a response that I posted here, maybe 8-12 months ago. Someone else raised the issue more recently that the State Police don't have jurisdiction further out in the EEZ waters, so Fed laws apply, and I don't think there was any resolution on that.
Bottom line, with the state laws, my (non-lawyer) interpretation is yes you can take your firearm of choice on the boat and use it to dispatch sharks, as long as you are otherwise fishing legally (size limits, species, etc.) and following the other regs about transporting firearms (unloaded during transport, etc.).