Our solution, having 3 TVs, the main in the living room, one in the kitchen and one in the garden room is to have 2 sky extension mini boxes connected via a couple of Sky wifi extenders (connected to the sky boxes not our broadband).
Without being a technical expert, I'd suggest that 20 feet thorough 2 walls with an HDMI cable from the Sky box to the screen may be stretching it. You may also struggle to control the channels on the Sky box through 2 walls if you are sat next to the screen with the zapper.