AFIK, it would have to be an official event, and a detour such as on a houseboat would get you a felony.
In other words, you go to the shooting competition, shoot, and leave. I don't believe that your type of plans would fly. I don't think there is a card, but I'd sure carry proof of registration or that I was signed up in a shooting event. The environment in CA is such that you'd be taking some chances. Depending on the agency and the officer, I'd say anything could happen. I've heard stories (make that read, as in newspaper) about cops confiscating perfectly legal handguns and when the owners give up trying to get them back, they give them to judges and da's for brownie points. When even cops have a hard time trying to buy an AW here, well, you can do the math. You could buy a FAB 10 Reciever I've been hearing about.
And I'd only shoot where you have express permission from a property owner or at a range.