Yep, cable is unnecessary. The right side of the handlebars has the thumb button. That cable goes down to the cylinder head. That has what looks like a valve in a car / 4stroke motor with the stem poking out of the head.
That assembly is on a spring that pulls the valve shut. The decompression thumb lever will pull the valve spring the opposite way, allowing the 'car valve' to let some of the combustion bleed off into the atmosphere.
as for the wires, they are color for color. Hopefully it wasn't too bad. It will get better. The first time took me probably a half hour, now its minutes.
Is your carburetor clean then? gas tank rust free?
after you get it running adjust the belt tension too.