One alternative is to use an HDMI switcher. You can get these cables for $5-10 from Hong Kong merchants. Here is the cable sold by an Amazon reseller: http://www.amazon.com/SANOXY-Switch-Switcher-Blu-Ray-HD-DVD/dp/B0040G5KY6/ref=sr_1_2?ie=UTF8&qid=1345843556&sr=8-2&keywords=hdmi+switch+boxes
I would imagine if you open the box, it should be fairly easy to have the arduino control the switcher by simulating the button press with an opto-isolator.
Then you can switch from the live cable to the 2 other cable slots. If for some reason you don't want to open (and possibly destroy) a $5 box, you could always use a servo to press the button (but then this forum is named device hacking).
In terms of HDMI breakout cables, I did a google search, and the first link wanted $60 for the breakout box, and it only seems to give you the DDC information (http://www.totalphase.com/products/video_hdmi/). However, given the Arduino is generally too slow with limited memory to deal with normal video, it would probably be like drinking from a firehose to keep up with hdmi.