I have a '80 Honda express NC50 so I don't know how to do your cables.
How to clean a carb well:
First take it apart and remember where everything goes. Make drawings and notes if needed.
Once you have it apart you should take off all the rubber and plastic. Remembering to take note of where they all go. Take out all the screws and then spay it with carb cleaner. You want to spray through the jets. spray and clean all of it, but focus on the jets most of all.
Some people feel confident using the high E string for a guitar, but you should be careful because this is dangerous. The metal the carb is made of can scratch pretty easy. If you don't feel confident then use a nylon stub from a nylon brush to physically remove the junk inside.
Blow through all the tiny jets as hard as you can and then spray it again and repeat this process until you think its definitely clean and then do it two more times to make sure.
Soak the carb without the rubber and plastic parts (screws if you want) in carb cleaner over night.
repeat the spraying, picking and blowing again. If you have an air compressor this helps a lot. spray some compressed air through the jets.
then put it back together. Get used to it because you should clean your carb every six months AT LEAST.
Good luck and get scrubbin'