Three ways to do that.
1. Run a cable from your dish or multiswitch (or SWM splitter, if applicable) to your backyard and put it in a weatherproof outlet box. Trot the box outside and wire it up. (this is my solution. I have both cable and DirecTV, so there's an AB switch upstream that makes the cable either BHN or D*. Just gotta remember to remove the terminating resistor before switching to DirecTV)
2. Do the same thing with HDMI cable as you proposed (more expensive) and use the RF remote feature of your box for channel changing, if it has that. You'll need a new remote, possibly.
3. There is a wireless HDMI solution, but I've never tested it.
Walking the fine line between jaw-dropping and a plain ol' yawn.