Connecting an exterior string of patio lights to an existing permanent exterior CFL fixture
Of course, the &quot;best&quot; thing would be to get approval for a licensed electrician to add a switched outlet outside. Or use a remote-controlled outlet, some even have regular-looking-but-wireless wall switches you can stick next to the light fixture's switch with removable adhesive. Or maybe invest in some alexa/homekit/smarthings junk.
The socket cannot be adapted, the cfl gets high voltage from the transformer. I might consider ripping out the transformer and cfl socket, then putting a normal ceramic bulb socket on the bracket. Many sockets have the black and white wires pre-wired; just match them up with the leads show using wire nuts or wagos. Might need some epoxy or jbweld to attach the socket to the bracket, depending on how it attaches. It doesn't have to be very sturdy, but it needs to be able to take some heat, so no hotglue.
It would then be fully functional with CFL/LED bulbs and nobody would notice or complain. At that point, a simple &quot;socket-to-plug&quot; adapter would give you a plug for a DC adapter for your LED strip. Use an inline GFCI if possible. I don't know how you would hide the wires and keep the wall wart dry, but I think this idea at least solves your wiring issue within the confines of your HOA and pre-sale home inspectors.