How do I unstick a sticker?

Try butter, I find it usually works. Full fat dairy butter, the hard stuff. Massage into the gooie sticky bits, might take a few minutes but I always have success. Good luck.

You probably need something like white spirit. Whatever that is.

Oh yes! Nelliemoser has already suggersted that. (I didn't like to mention meths)

I use furniture polish to remove sticky labels. I was told that in Germany and I have found it works.

Some years ago I bought a prancing Beswick horse from a charity shop that had suffered multiple fractures to two legs and the " repair " had been carried out by a short sighted orangutang. I bought a tiny tube of" glue dissolve " from a local chandlers, oops, giving my age away, hardware retailers. It worked very well but not likely to be nearly enough to dissolve an area the size of a wing mirror. What might be worth trying is to go along to a decent hardware store armed with a magnifying glass, yes the tubes are that small, to see what the main ingredients are. If isotropic alcohol looms large, for example, lots of poundland type stores sell that in things like dvd cleaners, lens cleaner etc. Beware large bottles in these kits however, most unlikely to be the usually quite expensive isotropic alcohol.
A slightly more expensive alternative is to trade in said car and swear blind the mirror is in exactly the right place and go for a few pounds more for the " brilliant extras "
Hope the first suggestion helps but accept no responsibility for divorce lawyers cost for part two.
Cheers
Peter