If I understand him right, WC's argument seems to be that the President has the cons utional power to declare war. That's re ed. Nothing in Article II gives him said power.
That being said, I think there is a smart way of articulating his argument. The way Article I and Article II are introduced are very different. Article I starts with "All legislative powers herein granted shall be vested . . ." while Article II begins with a reference to "the Executive Power" which is vested in the president. Article II doesn't have the limiting terms of "all legislative powers herein granted." Instead, the Executive Power is vested in the president - and one could easily interpret Article II to suggest that there are executive powers beyond those granted by Article II.
An expanisve view of the Executives CiC powers also aligns with the history and design of the cons ution. The Articles of Confederation were problematic because they gave the states to much power, to the detriment of the federal government. The Cons ution was designed to remedy that problem by empowering the federal government over the states (e.g., supremacy clause). Part and parcel of that design was the creation of a national army and navy (which didn't exist under the Articles of Confederation) and the installation of the president as the CiC. I don't think you can assert 1) this history of the cons ution and 2) that the cons ution limits the President's war-making powers.
That said, the declaration power is contained in Article I - Article II makes no reference to it. However, I also don't think much emphasis should be placed on this fact. The quoted section of Hamdi also notes that there was no standing army in the late 18th century. IOW, we should understand the declaration power in light of congress's power to raise an army via appropriations. 200 years later, we obviously live with a standing army - therefore, I think it wise to de-emphasize the necessity or legal strength of the declaration power. In other words, I think it not uncons utional for the President to commit troops, without a congressional declaration, to foreign military hostilities.
An other argument could be made as follows: if Article I supposes full congressional (meaning House + Senate) assent to military operations, the President would be unable to quickly mobilize troops to military operations. Neither Article I or II makes reference to the need (or lack thereof) of congressional authorization in the event the US is attacked. In other words, if you think that the Cons ution requires the President to obtain congressional authorization every time the military is mobilized - what happens when the US is attacked, and congress does not approve military action for hours or even days? Is the President supposed to sit back and watch?