Since there is a time limit to edit my original post and I cannot anymore - let me add this to update and clarify:
On my engine, '98 50HP Johnson with remote controls, electric key start and steering wheel, the kill cord isn't required. If missing, no problem to run the engine, you just don't have a kill cord.
If connected and pulled, engine stops. Engine can be immediately restarted without kill cord.
This is by design for this model, as after replacement of entire switch/key assembly the problem continued - the engine would restart without lanyard. My dealer said they had to do some research and found out this is standard for this model, even he didn't know and thought it was a wiring problem.
I actually prefer the engine to be restarted after pulling the kill cord; just falling overboard while at speed could pull the kill cord off and let it sink or blow away. Loosing the kill cord could leave you totally stranded at sea without a way to restart the engine.
I recommend sailors test their kill cord somewhere safe - close to a dock or while running at home, not out in the middle of the harbor- and learn how to reattach the cord. My kill cord is a little tricky the way it snaps back onto the key switch, the ignition key is at an angle and low, hard to see exactly without reading glasses. Its easier to reattach standing next to the boat.
What I wanted others to know is that not all missing kill cords shut off the motor forever...this was what I learned, and although it worked, the switch was sticky enough the boat may have ran for hundreds of yards before vibrating open, leaving me too far away from the boat to return.
I hope this helps.
I'm very concerned about safety being a pilot and former USN submarine sailor (stationed in Holy Loch!).