For a short run like you are going to run, I can't imagine that a consumer grade coax will be any different then a 'supposedly' higher quality run. Just take your box outside, and be done with it. A HDMI that long will be costly, and you probably would not use it for anything else. You can buy some raw coax, and the ends, and just cut it and make it yourself, I have done it dozens of times.
-- Neil --