no this is the wrong way, correct way would be something like this "can you not smoke for three days?......"(there could be a better sentence but i had to use 'can' or 'want')

Can you go three days without smoking? You shouldn't say: "Can you not do something."

Correction: "Can't you stop smoking for three days? No, I can't. I'm addicted to it."

"Can you not" is incorrect English. You can use "Can't you ... ". e.g. : Can't you refrain from ( / go without / avoid / stop) smoking for three days ? If you need to use Can, you need to use it this way : e.g. "Can you refrain from ( / go without / avoid / stop) smoking for three days ?" the difference between the two is "can you" is asked as a request where as "can't you" is more authoritative (and has a more assertive tone) than "can you". Though both have the same meaning. A third way to say the same thing is as follows : "You can stop smoking for three days. Can't you ?" this means the same thing but has a slightly positive tone of believing that the person can stop smoking.