The Canadian Shaw Direct service is available in the US but will not work with your King Dome. You will need a full sized open face antenna exactly those you see on a home or business.
In the US, you can sign up for service with DirecTV or Dish if you have a US address to use and a US credit card (or you could buy a reloadable CC). Dish has a pay-as-you-go service allowing monthly service. DirecTV requires a 12 or 18 month contract but can be suspended for up to 6 months at a time (extending your contract period by the suspended periods).
Both DirecTV and Dish will work with your King Dome. You cannot receive the DirecTV HD programming with your dome and depending upon the age of your King Dome, it may or may not allow you to receive the HD programming. The KD must be capable of pointing to the 129 and not only 110 and 119 for Dish HD.