As far as I can tell, the extra wire is the actual antenna for the radio.
The wires with the porcelain/glass insulators that go from the wintergarten to the stern, and the CT front to the bow are "jump cables" and they have two purposes. The insulators themselves are almost the same as the insulators that you sometimes see between the cable from a telephone pole and the stake in the ground that it's attached to.
The first purpose is to act as a support for the radio antenna/wire. It is for this reason that they have the multiple round insulators to separate them from any interference with the hull. It's easier to see at the forward end of the CT, but there is a very thin wire, the actual antenna, that comes off of the jump cable just before the insulators and hangs loosely underneath to enter the front of the CT, usually slightly to starboard but sometimes almost in the centre of the CT. As it goes along the jump cable, the antenna either spirals the cable, or is attached every so often by a clip.
At the aft end of the CT, there are two horns, one on each side of the wintergarten, and the thin antenna wire again comes off just before the insulators and goes into the horns on either side. I think the small wire you see underneath the jump cable in your picture is the antenna wire and it's a bit thicker there because it's insulated to stop it from shorting out if it touches the jump cable.
The jump cables themselves are not what picks up the radio signal, but just the support for the antenna.
The second purpose of the jump cable (and this is more important with the bow jump cable) is to deflect any anti-submarine nets, cables or foltsam so that it doesn't entangle the deck gun, schnorkel, CT, periscope or any other projections when the U-boat is near the surface. For this reason, the jump cable is fairly thick and strong, and stretched fairly taut by turnbuckles at each end.
