It works. Success.

Any actual electrician is going to be bored by what I just pulled off but, as for me, electronics used to be a mysterious black box I didn't even begin to understand and fixing something instead of throwing it out and doing it myself and actually succeeding fills me with excitement. It's true, I did need an AI to fill in some gaps in my knowledge. ChatGPT helped me find a Product that would fit and replace The Broken knob that was injection molded and fell apart instantly. Seems corners were cut during manufacturing, like, rock solid motor and fan but cheap plastic knob and crappy molded cable. Now, I know why Electricians swear by Levinson plugs. It also taught me about Caliper's and I picked up on how to use them very quickly in order to take the measurements it needed to find me a product.
Diagnosis: Electrical plug broke because of Flex physics, owing to the reality that it was my on-off switch, since the knob broke.
Fix: New plug, and New knob.

I did the hard thing instead this time and fixed the broken device. Gained a bunch of new skills along the way.

Gained new insights: A pair of helping hands for Solder techs would have made this job easier.