Put tv connector with tos link in your tv. Sound for others will be unaffected, and you’ll have your own in aids directly.
Roger select with his cradle I think can do the same.
However, in aids, they use different programs - tv connector uses tv program, select uses roger program.
By default they’re set up a bit differently.
Also could be further adjusted.
If you intend to use select as a mic, I’d recommend using tv connector for tv, and have those tweakings that your fitter will do, separate.
Plus, select sends mono, tv connector sends stereo.
Edit: just realised that you didn’t mention tv connector, I’d highly recommend it because of things above.
Also with BT to tv, unless tv supports splitting the BT signal, and you have BT speakers for others to listen, I don’t think it’s possible.
So far I only know that my phone (s8) supports bt splitting, and it loses volume, but I don’t know about other phones or tvs which do that.