Where it is written, "Some will say you have faith and I have works. Show me your faith without your works and I will show you my faith by my works." This seems to be answering in a way that is saying, "It is possible that you have works without faith, since you cannot 'show me your faith,' but it's impossible to 'show' my faith without works, since, again, it's not possible to 'show' faith, except by works....
Let establish the exact claim of the OP, here. Is the argument that one "must have works to show faith, and so then the lack of works shows a lack of faith" with the understanding that faith cannot be 'shown' at all apart from works, and that, even if it is invisibly present, it cannot save unless there is work to show it.
If indeed this is the argument, what then do we do with the reality that there are actually works without faith present.
I'm sure it is unanimously agreed upon that works without faith is insufficient to save, as works do not produce faith since faith must come by hearing and hearing by the word of God. That is faith is not inherent to works.
Now then, if faith comes by hearing and hearing by the word of God then faith does, as is inherent to faith, produce works.
So, the question posed that, "if a person says I have faith but has not works, can that faith save him?" seems to be a rhetorical question calling the claimant a liar, since faith, hearing the word, produces the work of a 'new man.'