Pick up the tab? Not me! (3-6)

I believe the answer is:
non-smoker
'pick up the tab?' is the definition.
I don't know anything about this answer so I cannot judge whether this works.
'not me' is the wordplay.
'not' becomes 'non' (I've seen this in other clues).
'me' becomes 'smoker' (I can't justify this - if you can you should believe this answer much more).
'non'+'smoker'='NON-SMOKER'
Can you help me to learn more?
(Other definitions for non-smoker that I've seen before include "One who doesn't light up" , "Person not inclined to light up" .)
