Well the 80s K bikes I think had a 17 inch rim, same with the 77/78 K. Now if you went earlier, then those were 18 but I am not sure if the axles were the same. Both are drum brakes I think, I know the 70s K were but I am not sure about your C. If it is, then you might be able to make the swap but again, the axle size might be different BUT you CAN get different bearing sizes that could compensate.
The ride IS the adventure. The destination is just to get gas!