Has New Horizon's data updated Charon's orbital elements?
I suggest you use the JPL Horizons system. You can investigate how Charon's orbital elements change with time. The short answer is, not surprisingly, not by much. The values for the eccentricity I see hover around 0.00015 and those for the orbital inclination relative to Pluto's equatorial plane are about 0.09 degrees. 

http://ssd.jpl.nasa.gov/horizons.cgi