It might be best if you were to post a picture of your petcock.
Most of us are in the US and the "C" model was never sold here, so is quite rare to us. Further, our usual sources of info, the fiches and manuals, don't cover the "C" model.
If we see your petcock we may be able to give you some advice on fixing or replacing it.
The KLR650C has a petcock that is backwards from the "A" and "E" models in that the outlet is forward of the petcock rather than aft, and the primary tube is probably (should be) shorter than the "A" and "E" both because the petcock is farther back in the tank where there is less vertical room and because the tank is about 2/3 the size of the "A" and "E" tank.
A Yamaha Raptor 660 petcock might be a replacement solution, as its primary tube is quite short. I don't know if hose routing would be a real problem, though.
I will go look at an "E" petcock and see if the hose can be easily switched.
Here's a picture of the "E" petcock vs the Raptor.