Gear or direct drive?
On a lawnmower or an outboard motor, a cord works because there is a flywheel to which the cord is attached. The purpose of the flywheel in those examples is to make it easier to pull. The flywheel in those examples works as a gear, which means that not too much effort is needed to start the motor. Which is why you perceive it to be easier to pull a cord.
The whole point is that the diagram shows a cord attached to the drive shaft and as Patrick pointed out originally, relatively the flywheel looks rather heavy. It doesn't make sense to use a cord to start it. It will require much more strength than a lawnmower. Do you have a car, or a bike? Do they have gears or are they direct drive?
In the Hamada example, there is a weighted flywheel underneath the working surface. His wheel was a pre-cursor to the kick start wheels that you refer to. He managed to work out that by pushing the edge of the wheel, it required less torque or strength to turn the wheel than to put crank it from a central drive. This is also a form of gearing. Imagine if he had a hole near the centre of the wheel to put his stick into. Which would have been easier?
You are quite right, attaching a string to the pedal would not work. Well spotted! As you say, you would need to attach the cord to the sprocket, which, again is a gear!! Maybe, what you should do is to attach a piece of steel to the axle of the bicycle and then wrap the cord around that. See if you get a better result than spinning the wheel from the edge.
I am not really an expert in this, but so far as I know, direct drive requires more effort than gears. But I am not an engineer, so I am not going to add much more. Instead, I am hoping that there is an engineer out there who will be able to confirm that it would require less effort and torque to spin the fly-wheel from the edge, rather than pull the cord.
However, I would be equally happy if an engineer can show that that pulling a direct drive cord requires less force. Smiley
I would also be very interested for that engineer to provide an explanation that shows that a using a cord would give a more constant speed than spinning the flywheel, because my very basic memory of studying this stuff about 35 years ago is that the fluctuation of the speed will be primarily related to the weight of the flywheel and any variation to the speed will be related to that as soon as the force is removed. In other words, when you stop pulling the cord, or spinning the flywheel, the deceleration will follow a constant curve.