A lot of the issues with regards to the Falklands would go away if you just made sure it was included as part of the UK in NATO. I think I got that right, NATO doesn't get involved or something along those lines??? Obviously a bit harder in practice (dam politics), but it would mean Argentina wouldn't bother militarily anymore.
When the North Atlantic Treaty was agreed in 1949, UK and France, inter alia, had considerable number of Colonial possessions, that would have impossible to have protected under NATO. Moreover, the US was virulently anti-colonial and it would have been very unlikely that they would have gone to the direct aid of a NATO member in a Colony; Indo-China/Vietnam (5 years later) notwithstanding.