You will find that Sami does not use ø, and nor does Swedish. The only languages that do are Danish and Norwegian, and Føroyskt mál which is most definitely not connected geographically to anything Scandinavian.

Denmark and the Faroe islands are not in the Scandinavian peninsula. Only Norway is, of the countries with languages which use ø.

Scandinavian, as language, in modern times encompasses Norwegian, Danish, Swedish and Icelandic, with Føroysk as a minor language. Three of those use ø, meaning it is more correct (though still incorrect) to speak of them as using ø.

If you by "geographically bounded Scandinavia" mean the Scandinavian peninsula, your rule of thumb is incorrect.