Seriously, do you really think it's worthwhile to do this?

Maybe a work around might be better. How about a amplified computer speaker instead? As a tv repair tech, you know you need a schematic diagram first. Assuming you can get much you think it will cost. Personally I have my doubt about the relay. A relay in the audio circuit kind of leaves me scratching my head. Anyway, I just don't think it's economically sound..that's all.