Yeah but I think for that price the OP should consider the Apple TV (even a second hand 2nd gen would do, although those are expensive now since the ATV3 is not jailbroken yet). $99 bucks and all you have with that plus AirPlay.
If they sold a cable for 10 bucks, then obviously ATV would seem like a stupid choice unless the OP wanted one.
Also AirPlay streams it all, while the cable just video and some apps as far as I remember (not to say that the OPs wish is simply stream video from the iPod and that's it, but I throw the ATV option out there for consideration).