Is there a shooting range there, if so I'd just tell any cops it's for there. Nah seriously though I'd just call the place you pay at for the camping spot because they should know/be able to tell you specifically. Even if it's not legal to open carry or CC around the park I'd keep one in the truck personally. Too many sketchy people out there along with plentiful amount of thieves.
Just my idea/opinions so no responses on morals or always obeying laws no matter what please!