Tax implication for Canadian owning a LLC
You most certainly can register a US LLC and obtain a US EIN for the business. Under US law an LLC can be what is called a "disregarded entity". That just means the LLC itself does not have any US federal tax standing and the IRS will look to the sole owner of the LLC in determining how the income of that LLC should be taxed. That means having a single owner LLC in Wyoming would not change your tax standing for US federal taxes. That does not mean you are not already subject to US income tax under the US/Canadian tax treaty, which would require a much more in depth analysis of your business operation than what I can provide here.
While Wyoming does not have a state income tax it does require you to pay an annual LLC annual fee, there also could be sales tax obligations in other states which is also beyond what I could cover in this forum and would not change just because you set up an LLC in Wyoming.
You would not be able to sell at zero profit, due to what are known as transfer pricing rules, which establish how related entities located in two different taxing jurisdiction must establish the price they charge each other for items that are transferred between themselves. As a disregarded entity transfer of goods is irrelevant anyway because the LLC and the owner are seen as one entity under US federal tax laws.
That is just from a US tax perspective and you should know that Canadian tax law does not necessarily treat US LLC's the same way the US law does.