Do not take out any clutch springs, that will cause problems!
Go to your local bike dealer and get a "cable luber" they are made by motion pro and other companies similar. They basically attach to the cable and you can get a can of spray lube and attach it to the luber, then just spray.
Your other option is to get a new cable, but I feel that with the bike being that old the cable has worn and is dry. So either lube it or get a new cable.
This will be the most effective :thumb: