If the shifter is still consistently clicking through the same number of stops, it is unlikely to be the shifter's fault. The cable position is decided by a discrete number of teeth or détentes, and there is very little wear possible that could effectively move the position of the détentes.

From your description, I think the two most likely culprits are cable friction (it doesn't make much sense to change just the inner wire as the housing is usually where excess friction is caused), and derailleur hanger alignment. Other possible causes are a very worn chain, or a derailleur that is worn or damaged to the point of being sloppy.