The fastest RC servo currently available is the Airtronics 94758Z.
Servo speed specs are rated by TIME/Degrees traveled, so this one , being rated for 0.06(sec)/60 deg means that the fastest possible move for 60 degrees will take 0.06 seconds which if repeated continuously would be a frequency of 16.6 hz. Obviously , if the fastest servo sold is 16.6 hertz for a 60 degree movement, you can kiss your plan of getting it to operate at 200hz goodbye. That's a pipe dream. Not possible. A medical EEG does not use RC servos, so your plan to build a working EEG chart recorder using hobby servos and Bic pens is, well, maybe not flawed, but perhaps a little under researched. I don't know if you have ever actually seen an EEG chart recorder up close and personal, (I have, I was a medic in the AF and worked in a hospital ) but they have very delicate needles (the old mechanical ones , designed and build many years before you were born) and one of the reasons is the energy needed to move some mass is proportional to the velocity and mass . An RC servo arm has a much greater mass than an EEG chart recorder needle so the torque needed is much greater. The needle , moving 3 cm (0.03 meters) in 5mS (200 hz) is dist/time=velocity===> 0.03m/0.005mS=6 m/S . The fastest servo available is 3 cm (approx 60 deg) ===>0.03m /0.06S=0.5m/S , which is 1/12th the velocity of an EEG chart recorder.