if i were you i wouldnt touch the pickup with your soledering gun incase you break the wire that wraps around the pickup.
but what you could do and i have done in the past for a quick fix , is join you pickup wires to the old pickup wires.
cut them and remove a little plastic/cloth covering. twist the old and new wire together drop a bit of solder in there and tape it up.
that will work. its not a pro job tho.