A fully wired and screened scart cable between your STB and TV should do the job just fine, even better if you can use RGB.
The stereo sound will also be carried to the TV and output through the TV's speakers, if you then want to feed a seperate amplifier use the TV phono outputs (If it has any) or use a scart cable with additional phono audio outputs.
A scart cable from your STB ending with three phonos (2*audio and 1 video) would indeed reduce the picture quality.
Just checked
Maplins , they have the cable I am thinking about.
Scart to Scart with an additional 4 phono outputs...Code VA23A