This is pure semantics here, but no-one here ever refers to the 10 May 1940 event as the "Invasion of Iceland", but rather uses the "friendlier" term Occupation, seeing as out of the two warring parties, everyone except the Communists (who sort of supported Hitler until June 41 due to the NAP) gasped a sigh of relief that it was in fact the Brits and not the Germans that came here first.
@Putin: I need to address some of your points. a) Language: Official language aside, it was not used by the general population in Iceland, even though many of the upper class learned it. The modern grammar you refer to was indeed written by Rask, a Dane who had learned Icelandic by himself, which was considered then and now to be a huge feat. The two languages are very different despite both being derived from Old Norse and not easily interchangable. This whole discussion dances around the fact that Iceland is verifiably not Danish in its cultural makeup, genetics nor heritage and gained little in being a "possession" that the Danes didn't really have an interest in.
b) I can sympathise to a point with your ultra-realist position and which equates sovereignty with Hard Power, much like Stalin asking how many divisions the Pope had. However you cannot measure the world completely in those terms. The international system isn't a mad free-for-all, in spite of appearances.
"Scotland has plenty of autonomy over its own domestic affairs. So does Gaza. So does Catalonia." But all of these have to eventually buckle under another entity. If Scotland decides something that Westminster can't abide by, Scotland has to yield. We don't have to yield to anyone in any matter regarding our domestic policies. We have complete autonomy over our own domestic affairs. That's one part of sovereignty which you consistently overlook.
"As for Iceland having final say over foreign affairs, that's based on the goodwill of its allies." This could probably apply to each and every other country in the world today. No country can really do whatever crazy thing it dreams of without being kept in some sort of check by the international system or its allies. To take an extreme example: Could the UK use its nuclear weapons on a whim? Can the UK on account of its nuclear weapons impose its will on other nations? Even with their substantial military, they too would probably have to yield to the USA or the EU on every issue if hard power was the only factor in play here.
Our lack of armed forces has not prevented us from unilaterally expanding our fisheries in the fifties-seventies ("Cod Wars") in spite of most of our allies, including the US, UK and FRG opposing us. If in fact we are not sovereign and should just be Danish like you say, then why didn't Britain and West Germany somehow manage to enforce their will upon Iceland? The Cod Wars are an important example here, because it is sometimes used as an example of the limits of hard power. You could also examine the more recent issue of the Icesave-dispute between Iceland and the UK.
I won't deny that Iceland has sometimes tried to swing above its weight in international issues. But the main fact cannot be overlooked, that on many important issues, Iceland is able to make its own way in the world as a sovereign nation... lack of an army notwithstanding.