[Scott Fraser]

Graphite sounds reasonable. I would hesitate to put a soapy liquid
near a
piano's finish.

It wouldn't be anywhere near the finish. Usually the squeak comes from
the point of contact between the back of the pedal & the lifter rods,
or between the top of the lifter & the damping mechanism. Harder to get
at is the axle which the pedal rotates on. It's generally at a point of
metal to leather or metal to felt contact. Common sense should allow a
safe application of the graphite.

Scott Fraser