I use my Craftsman, 18mm, six-point, deep-socket. The socket was part of my 154 piece Sears socket set. It isn't listed as a thin walled socket, but it fits.
I suggest finding a piece of rubber tubing that will fit snugly inside the socket. It will grip the plug while you pull the socket out.
Also, don't forget the anti-seize compound.
Have you figured how to get at the number two plug yet?