I've tried Bluetooth speakers with TV and computer media players. The latency's bad enough that you see someone's lips move, or the gun goes off or whatever then..........after........a.........while...........you hear it.
It's quite possible there's better stuff about than I was messing about with, in fact I'm sure there is, but I found the latency made things unwatchable. Maybe because like most musicians who've played in loud bands where you can't easily hold a mid-song conversation I can lip read a bit. Whatever,s I find it the opposite of comfortable, so wired it has to be.
There's quite a bit of stuff on the market aimed at improving TV audio for people with less than perfect hearing, may be a better idea to investigate that. My late father had a setup 15 years ago he reckoned was pretty good, it communicated with his hearing aid earbud like hearing loops do.
Edit - just a thought, but if the TV setup has an audio or optical out and you happen to have some headphones and a suitable device for connecting the two...... :-)