I fixed my problem. The C buttons are now working. What I had to do was actually delete the actual game file (Conker’s Bad Fur Day (USA).srm) found in the saves folder. I remapped the buttons to my Xbox 360 controller in the regular retroarch input settings and when I loaded up the game the buttons were automatically mapped to the 360 controller, including the C buttons!
When I tried the same thing with my USB N64 Controller, the C buttons worked but all the C buttons also had other actions assigned to them along with the cameral controls. Which is weird…
But anyways the Xbox 360 Controller works perfectly!