Thanks for the elaborate answer!
I see the Retro Access cables actually input the audio at the console side, which absolutely makes no sense if you’ve decided to go for a separate NES audio output. However, that Scart adapter you’ve linked to, that might actually be a great solution.
Also, I read in the Retrogamingcables Pakapunch product description (that’s the cable I’ve bought) that there should be enough shielding to route audio through the cable anyway.
So what I’ll probably do, is route the audio through Scart, but via a switch, so I can switch it off whenever I feel the need to use an external audio cable anyway.