Oh I didn't know that about Danes! But I think that's where it comes from too, since we also call the city as Wien (Finnish rarely changes the original names of cities, usually only to make them easier for us to pronounce) and Wikipedia says the pastry is called either viineri or wiener in Finnish. Since we don't have the letter w here in Finnish words and it's anyway pronounced like "viiner", it was only natural to come up with the word "viineri".
Nice info! I hope the future tips will contain this tidbit of information.