have not done it but have been looking into it for the same reasons.
Moving the cable would require some pretty twisty routing (and standing on your head in a phone booth to do it).
The electrical solenoid is avalable and is about $50 plus the push button and 12 volt control solenoid (auto part, little black square 30 amp relay). The yanmar manual has the part numbers and not just any old solenoid will do. These things have to be able (my engine) 20 lb and a 1" stroke.
from page 9-43 of the 4JH2E service manual
solenoid type 1502-12A7U1B
rated voltage 12 volts
loaded current 30 amps
loaded force 9 kg (19.8 lb)
no-load current 0.7 amps
no load force 4 kg (8.8 lb)
should bolt right on if my eyeballs and the diagrams are correct. The wiring has high current from the mains supplying the helm station which leads to the 12 relay and then to the solenoid. and ground return of course. The control wires go from the ignition key to the push-button to the control side of the relay and back to ground.