Since this is the accepted answer, I can't delete it. But after another decade of DIY work, I agree with the comments below. This is not code, and not safe. Device power cables are not intended to be run in walls and are a fire hazard. IMO, @gregmac's answer below is correct, provided you use proper electrical cables in the wall (as gregmac notes in the comments).
@Jeremy has a good solution, but if you're willing to do a little more work, there is a little better-looking answer. Since you're running an HDMI cable, I assume you have some kind of small stand/table in front of the outlet that your cable box sits in or on.
With a drywall knife, punch out a hole behind the TV and install a plastic "old-work" 1-gang box. Don't worry, we're not going to install electrics here; just a plastic box that has a couple of "ears" on it so it can slide into existing drywall. Do the same thing at the bottom of the wall, above your electrical outlet. You can now run the cables easily through the wall without patching any drywall. If everything's laid out correctly, both will be hidden (one by the TV, one by the stand/table that holds your cable box).
If you're just using a regular outlet as you suggest behind the TV, then my suggestion would be to supply it like a regular outlet.
If there is another outlet nearby (directly below would be ideal), fish a wire to it, and attach it to that circuit.
If there is unfinished space below, you can get a wire down there (use a long "installer's drill bit") and then it should be relatively easy to find a circuit to attach it to (or just run it back to the panel).
I'd be nervous about any contraptions that attempt to get power to this circuit otherwise. You absolutely need to have a male end in the wall, as a male-to-male extension cable is dangerous to have.
The best thing I can think up totally as a DIY without requiring real hard-wiring would be to get a blank faceplate, and put a square hole in it, and then mount an IEC 320-C14 connector in it (eg. from digikey).
Then you can just use a standard C13 cord (like the kind used to connect most computers, TVs, etc) and plug it into a surge protector or UPS or whatever.
Best Answer
I would treat an inconsistent reading as a positive (live wires). The reality is, it's hard to detect with 100% confidence an actual live wire behind a wall with a stud finder or non-contact tester as these can be triggered by low voltage lines, or line-voltage lines that are off but in close proximity to other live circuits. The proximity of the wire to the walls surface is also a factor here.
Wires running vertically should be stapled to the stud so you are less likely to hit them when cutting into walls, so it's really the horizontally run cables you need to worry about.
An inspection camera is a handy device for these scenarios since you can look around the stud cavity to confirm or rule out the presence of electrical wires.
I'm assuming this is because you want to cut into the wall. If you think there might be wires behind where you are cutting, instead of using a drywall saw, try just scoring the drywall and give it a good whack with a hammer to break out the piece of drywall - you're far less likely to damage wires or other infrastructure this way.