In Canada, can I run Ethernet cables through air ducts?
In Ontario, Rogers spent years running their coaxial cables through duct work. The only downside was that the heat caused the wires to wear more quickly.  I don't have access to codes here, but if Rogers did it then it's probably allowed.

Ethernet cables aren't shielded as well and would suffer the heat more.  Maybe run them through the cold air return?

As an alternative, if you can get he cable to the right floor, stapling them to or behind baseboards worked well for me.

Hope that helps a little.