I'm afraid your original premise that works have nothing to do with salvation is, simply put, nonsense.
Your objection to James's relevance here is poorly founded.Even if we take it literally that his letter was addressed only to Jewish converts, there's no reason to not consider it binding on all. Do 1 and 2 Timothy not belong in the Bible? They're addressed to a single man who died nineteen centuries ago. No, I believe as Paul told Timothy that "all scripture is given by inspiration of God, and is profitable for doctrine."
But let's explore your premise more substantially. Is it true as you say that "works [have] nothing to do with salvation?" Certainly works are not sufficient; that's Pelagianism. But are they necessary?
Jesus seemed to think so. He taught that there would be a division between the saved and the damned based on who carried out the corporal works of mercy (Mt 25:31-46). Jesus also warns us to "abide in [Him]" lest we be cast off. (cf Jn 15:4-6) How do we abide in Him? We keep His commandments (Jn 15:10). Thus, it is clear that action with results external to ourselves (aka, "works") is necessary for salvation.
Paul teaches that salvation is through faith. But what is faith? What is Paul's purpose in Romans? To bring about the "obedience of faith." (cf 1:5, 16:26) So clearly, as James clarifies, there is a necessary active component to this thing that saves.
Paul certainly doesn't teach that faith alone is sufficient. See 1 Cor 13:2: " [T]hough I have all faith, so that I could remove mountains, and have not charity, I am nothing."
Even your original citation is misleading, for it leaves off the next verse: "For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them." Do you think we can disregard what we were made for and still be saved?
Let me be crystal clear. I am NOT saying:
-that we are saved by works alone,
-that works without faith are profitable,
-that salvation is earned through works,
-that we deserve salvation for any reason.
I am only saying that since obedience is an integral part of the sort of faith that is good for salvation, the products of that obedience, which we can generally call "works," are also necessary.