Working on small engines is not your cup of tea... if it is just for seelling something not that good repaired, sold it as is and take money to have a beer, it can refresh mind
Guaranteed to start is for a maintained engine, not for something sleeping in rain with no love (or at least basic maintenance) to give it.
By the way, a throttle is almost useless on a (small) push mower, to idle at 1800RPM and mow at 2800 this is a a more complicated carb control, a cable, a lever for almost nothing but cost.
And as said above unless you have a blade clutch (that cost and wear out too) law need the engine to stop within 3 seconds when releasing handle - basic safety.
Anyway hope you have success with you repair.
Every thing that adds a complication also adds another potential problem.
Outdoor equipment makers are being held hostage by the pollution Nazis
None of them want to fit auto chokes they are a lot more expensive that a few feet of bowden cable and a thumb lever or over reach lever on the throttle control.
Auto chokes give me a lot of grief regardless of what brand or what piece of equipment.
If you remember your physics, liquids get more dense as the temperature drops.
And metals contract as they get colder
Below 40 deg, the contraction in the main jet in the carb can not account for the increase density of the fuel .
This has the same effect as fitting a bigger main jet and allows the engine to run richer, closer to what it should run.
However running at a proper fuel:air ratio puts the exhaust outside the allowable emission limit so you the customer get told not to run the engine below 40 deg.
The engine will happily run down to around -40 by which time fuel will not flow under gravity at -60 the fuel will freeze in a metal float bowl.
But as your mind appears to be closed you will never be happy with the unit so sell it as soon as possible to some one who will appreciate the equipment.