If you wanted an external solution you could try a Live Gamer from avermedia
I used to use Fraps, but it crucified my PC and gave me crap frame rates to boot.
Not cheap, but won't affect your fps, and can stream to YouTube or twitch.
I'm using this.
http://www.amazon.co.uk/gp/aw/d/B00C1EO536/ref=mp_s_a_1_1?qid=1397640526&sr=8-1&pi=AC_SX110_SY165
You could of course use it on a console or anything else with a hdmi out just as easily.
Play Claw is another option, I think it has a free trial, is on steam as well as direct.
Edit : Qualifier, won't affect frame rate up to 60fps, the limit of hdmi, unless of course you find a way of cloning the output whilst using dvi, but if already using hdmi you won't see a difference.