You don't say where in Switzerland, but for me the answer here is for surely, in a word, "via Italy"!
So, up from underneath rather than down from on top.
So, I'd definitely (1) drive first to Monaco.
Then (2) to Genoa (of course, one of the most amazing roads on Earth).
Then up through (3) any of the amazing cities in northern Italy (you could name 20 must-sees).
Then it's a matter of (4) "choose your pass" in to Switzerland, it's hard to go wrong.
Personally I love Aosta (who doesn't), stay there, and then go over or through the Gt St Bernard, to Martigny. Or just up through the lakes depending on where you're going. Or - how do you spell "Joy" - add merely a day and go to Bozen, stay in the best hotel in the world, and then continue up through himmel to Switzerland.
As I say, the southern approach (ie, "Italy") is James Bond all the way, it's all amazing. Travelling from Spain more to the top of CH .. we all love Bresse, Burgundy of course, it's really beautiful, but it's more "just" "stunning flat farmland" you know. And then if you look on a map driving from say Dijon to Basel, that part of the world, I mean it's not unattractive but its not like AND NOW LET'S HAMMER UP TO MILANO sort of thing.
Another consideration is, it's cool to go through the Frejus (so basically, like lyon or chambery to Torino), but, you know -- you wanna miss out on driving the italian riviera??
So, for me, in short, the obvious route from Andorra to Arosa, say (that's where you're going right!), is basically Andorra -> MC -> Genoa -> Chur!
Another short way to put this; it's much, much more attractive to approach Zurich from the south (Chur, etc) than from the north (Mulhouse, etc).
Hope it helps someone.
Again you didn't mention which part of .ch you wanted to end in. I realise this was a few years ago and I hope you had a great trip!!