Interior Designer is a listed Appendix 2 occupation, so the occupational half of the test can be met. The arrangement is the problem: TN requires prearranged employment with a U.S. employer that directs the work, and billing an American firm through a corporation you own reads as self-employment, which TN does not allow.
Where a consulting contract stops being employment
The distinguishing question is not what the paperwork is called but who controls the work. An officer will look at who sets the hours and priorities, who supplies the tools and the workspace, who carries the risk of the engagement, and whether you may take on other clients while it runs. Hypothetical example: a designer specifying hospitality interiors signs a twelve-month agreement under which her Quebec company invoices a Chicago firm monthly, she chooses her own hours and she retains three other clients.
That is a service business she owns, not a U.S. job, and no clause reciting that she is not an employee changes the analysis in the direction she wants. Two things can rescue a plan like this.
The U.S. firm can hire her directly as an employee, with a letter describing supervision, salary and worksite. Or the work can genuinely stay in Canada, performed from Quebec, in which case no U.S.
work authorization is needed for it at all. What does not work is presenting an ownership-based consulting relationship at the border and hoping the word contractor passes unexamined.