Good girl!
There's never a need to solder cords. A replacement cord is about $10 in the US and it has proper ends on it to connect to the electronic pedal. Hearing that, the pedal cord would be my first suspect. What was the pedal doing that it was a fire hazard? Properly adjusted, they're as safe as any carbon pile resistor pedal.
Don't forget to check the brushes too!
I still use the Singer lube because it's still available to me in the old formula.