Outside: Adding an outlet to a switched light fixture
How difficult would it be to run new wire to this fixture? You could tap into a grounded circuit and avoid this whole confusion. And if so, you can run an extra set of wires to go to your outlet, so the outlet wouldn't be switched.
Since the lighting box is mounted to your house, you can run romex into the back of the box (still considered indoors). Once the wire leaves the box and goes into conduit that runs to your outlet, you have to switch to THWN wire. Most THHN wire is also rated for THWN, so just look at the wire itself in home depot or wherever, it will mostly say THHN/THWN.