David, I have some questions. First, why do you want to specifically use “noise cancelling” headphones when you’re watching TV? Are there other sounds in the place (fan noise, etc.) that are interfering? If so, I suggest passive (closed, over-ear) headphones. Active noise cancellation cans produce a different noise at a wavelength that ‘cancels out’ your perception of the other noise, but both noises will still be producing volume into your ears. Passive cans simply seal out the outer noises somewhat, like noise reduction muffs (but not as much reduction). If you don’t have background noises to block out, then open-back headphones will do the job just fine (I like my venerable Sennheiser HD 600 cans, they have very faithful sound reproduction).
Second, why do you want bluetooth headphones when wired cans will reproduce sound more faithfully? BT introduces compression and other losses. I have a long extension cord for my headphones and have used this with my TV on occasion (but mostly I just turn on subtitles and be done with it). Be aware also that if you want the TV speaker to still produce sound (let’s say for bass effect or for the sake of others in the room), then you’ll need cans that feature a particular type of BT codec called APTX Low Latency (LL); otherwise there will be a lag between the main speaker and your headphones, producing nasty echo effect that muddies the hearing.