Why do you assume that a small fraction will have no effect?
Take another example: the ozone layer. How much of the atmosphere is ozone? You might want to look that up and tell us all. Also please let us know if the very small fraction makes ozone irrelevant to protecting us from the Sun's UV rays.
Another point regarding carbon dioxide: increasing carbon dioxide in the atmosphere also leads to more water vapour in the atmosphere. What's the number one greenhouse gas in the atmosphere?
The sad thing is that there are people out there that genuinely believe that the whole Ozone thing was a conspiracy bought about by DuPont in a profit taking exercise, because they had a bunch of patents relating to CFC's that were about to expire.