That pesky "C" is actually an "L" just rather fast and loose writing in this case; when you look at the tiff file of the label which the Internet Archive provides it blows the image up a lot you can see the L or WL et al in the run-out area.
I should say I couldn't find a C unless you spotted one I'd didn't see.
C was used by Decca for Chicago but only in the 9000 block until exhausted then jumping on to the 90000 block of numbers.
NY studio did not use a prefix as such, they started at 38000 to 39000 blocks and when they was exhausted moved to the 60000 block and continued from this number to the end of the 78 era.
The LA block stated at 1 with the prefix DLA, later just L or at least something with an L in it and got up somewhere close to 7000 by the early 1950's.