This is what I use, I have an older Bluethooth 4.1 version of this:
If your headphones are AptX compatible (all of mine are) then you won't have sound/video syncing issues. I have my Optik box connected to my sound system that has a headphone jack. I also have my TV optical out connected to my sound system as well on a different input so I can also use the Bluetooth transmitter for gaming or the Chromecast.
My hearing aids came with a device that connects to an audio receiver or TV to give Bluetooth. The sound goes directly into the hearing aids In stereo, of course. For music, I often pair over-the-ear headphones which also connect to the device. I know you can buy such a unit to get Bluetooth for a reasonable price.
My newer LG TVs have Bluetooth built in (Samsungs do too), so no need for those devices anymore. However, the best results are from my AppleTV. The pairing is much easier and the range is superior. Now that there is an Optik AppleTV App, I can use that most of the time to view Telus Optik, instead of the 5662 4K box.
I hope that information was somehow helpful.