As it's being run externally,i'd be inclined to get a HDMI over cat5/6 kit like this and either get some exterior grade cat5/6 or run standard cat5/6 in conduit. You wont have to make such big hole's in the wall as you will to get an HDMI plug through it.
Granted,probably not the cheapest solution, but neater/easier IMO.....
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