OP - I believe the following question will resolve the work permit issue:

Are you a 1099 or W-2?

W-2 = Work Permit not required. You will be considered as business visitor.

With W-2, you are an employee for the U.S. company selling the service. So the training provided can be considered as an after-sale support. Hence, no direct involvement with the Canadian labor market. So you can claim yourself as a business visitor.

1099 = Work Permit required.

With 1099, you are a contractor. So the training provided is basically a contract for you to perform in Canada.

IANAL.