Which type of coffee grinder is the quietest? Perhaps my question should be "What is the best type of grinder to use at my desk if I work in a cubicle and use a French Press?". 

I have tried finding decibel measurements on Amazon's website, but most of the coffee grinders listed don't specify them.
First, lets ignore blade grinders entirely.  Any grinder that doesn't have a motor will be relatively quiet.  You'll be at the mercy of the crunching beans, but that's it.  Add to this that the more the grinder weighs, or the more "heft" it has to it, the quieter it will typically be due to the additional mass damping any vibration.  When adding a motor to the mix, each step between the motor and the burrs adds an opportunity for noise.  As such, a direct drive grinder will typically be quieter than anything involving a gearbox.   

The pecking order is basically...

Hand Grinder --> Direct Drive Flat Burr --> Direct Drive Conical Burr --> Gear-Reduced Burr

While Decibel ratings are available from most manufacturers, they're difficult to translate into a subjective estimate of "harshness."  I deal with these regularly and found that some of my favorite grinders are technically louder than several others, including the Baratza Vario. The difference is that they have a much more mellow drone rather than the gear motor's quieter whine.