While I'm not suggesting that a mass parachute assault will be attempted by Argentina, the German capture of Crete in 1941 illustrates that it is possible to capture an island, despite a strong ground defence, without a large, highly specialist, amphibious capability in your navy.
Courage, daring, the willingness to accept losses and the use of innovative tactics can all ensure that so called "fortresses" can be taken, as has been repeatedly demonstrated throughout history since Troy (and probably even earlier).
At the end of the day the defence of the FI rests almost entirely on 4 Typhoons. If the Argentinians can establish and maintain air superiority over the FI the rest has a certain inevitability about it.
4 Typhoons is a pretty thin defence (I know, we will have reinforced by then as we know an invasion will be coming.... Yeah, like that worked the last time!!), which a smart opponent can overcome by a variety of options rather than direct aerial combat....
As for a Type 45 and an SSN, how often will they be down there? We will only have 6 Type 45s, and about 12 FFs, so 2 deployments out of every 3 for surface vessels probably won't be a specialist AAW platform. What price one type 23 against whatever the opposition elects to throw at it? SSNs are also pretty thin on the ground, and I'd be surprised if one was down there on a regular basis.
As for retaking the islands if we lost them, it is not just about military capability, but the political will of the UK PM and government of the day. Will they be willing to take large numbers of casualties, and potentially lose, in what would be a higher risk venture than 1982 without a UK carrier flying fixed wing assets...