To replace the headlight socket, you'll pretty much need to disassemble the whole power unit because the leads go through a top hole in the motor housing and then back through a side hole where the foot switch is attached.  All that requires removing the fan case and the bearing plate in order to access the motor.  The leads are covered with an insulation tube that is tucked down between the motor field and the motor housing.  The leads are also held in place by a retaining clip that's screwed onto the field. 

1) Remove the foot switch over.  2) Remove the screws that hold the outer motor housing in place and then remove the motor housing itself.  3) Once the outer housing is removed, remove the two long screws that hold the foot switch in place.  Once those the foot switch is free, then loosen the terminal screws on the switch and remove all the wires from the switch.  4) Remove the screw from the front of the safety switch (on the fan case) and remove then safety switch by pulling the wires through the fan case.  5) Remove the one long screw from the top-front of the fan case and then remove the shorter screws from the back of the fan case.  The fan case should come off now.  If it doesn't place the end of a hammer into the exhaust horn opening and tap gently.  6) Once you have the fan case off, you'll then need to remove the fan.  To do that, look through the slots at the front of the motor housing.  You'll see an cooling fan that's attached to the armature.  Spin the suction fan while looking through the slot.  Do that until you see a small hole that's drilled through the armature.  Once you see it, you'll then need to insert a pick into the slot and through that hole.  The pick will bind up against motor housing while you spin the spin the pulley on the suction fan off.  7) Spin the pulley from the suction fan off by turning it to the right (they are left-handed threads).  I sometimes have to use a vise-grip.  If you do that, however, I would encourage you to wrap a cloth around the pulley first.  8) Once the fan is removed, you'll see the bearing plate that's held on with four screws and star washers.  Remove those screws and then remove the bearing plate and you'll then have full access to the headlight wiring.  Sometimes, the bearing plate can be a little stubborn to remove.  When that happens, you can use a flat blade screwdriver and insert it through the vents in the motor housing and then tap gently. 

Hope this helps!

Also, you might be able to solder the sire back onto the socket.  However, you would still need to completely remove the socket.  Or you can find a brand new one on Ebay!  Before reinstalling the fan case, you'll need to remove any of the old caulk.  To do that, I just use acetone.  After removing the old caulk, I then put a bead of clear silicone around the fan case.  However, when attaching the fan case, be careful to get the holes lined up the first time.  You don't want to move it around while aligning it or it may mess up the seal.  Once it's lined up, the first screw I install is the long one on the top front.