Neil,
Are you sure it's the wire? The brass ring under the steering wheel on mine
caused a similar symptom.  A screw came loose and tore a piece out of it
causing a metal flap to short to ground. Ironically, after removing the
offending piece, the horn doesn't blow in the straight ahead position. I
need to fix this before vehicle inspection next month.
Ken Lewis
http://neksiwel.20m.com/