You can launch at the ramp by the bridge, but you need to get under the bridge to get to Banks channel and you have to wait for it to open. There is also about a 5 knot current there, so be careful.
You might contact The Ships Store. They rent spaces across from the Blockade Runner and might let you launch for the weekend.
Wrightsville Beach passed a law that you cannot keep a cat on the beach front over night unless you are having an event. You used to be able to buy a pass but a lot of sailors just left their boats on the beach and did not use them and after all the hurricanes some of the boats ended up in peoples yards and had to be removed by the homeowners (they were not happy).