Your argument is a little absurd. Congress could negotiate the treaty the same way the executive branch does: through the appointment of a trade commissioner.
Your expansionist view of the commerce clause is precisely the path followed by an expansionist court to destroy the concepts of separation of powers, federalism, and federal powers that are limited, express and enumerated.
The practical danger of your expansionist view of the constitution is illustrated by Clinton who used the Commerce Department and trade negotiations as a cash for trade deal with the Chinese.
My experience as a lawyer who has actually read the side agreements on NAFTA together with the WTO agreements and Bush Sr.'s Rio Declaration is that few people have any idea what the agreements contain. Are you aware, for example, that NAFTA and the WTO agreement embrace the Rio Declaration with its radial environmental positions such as "sustainable agriculture"?
Trade agreements have serious, long-term consequences for this nation and ought to be subjected to the lense of public debate and scrutiny. The process should be transparent, not one of "fast track" as is presently the case.
My argument isn't based on the Commerce Clause at all. And I have to laugh at those that say that Congress could appoint someone to do the negotiation for them.
They already did. It's called the Commerce Department.
Unless you or anyone else here is prepared to argue that Congress cannot create agencies to carry out the laws which it has enacted, then you have no argument.
By the way, I don't disagree with that. My position on this thread has been limited to the premise of this article.
We can, and have, discussed the merits of trade agreements on other threads. Interesting arguments can be made on both sides.