William, Argentina only had a handful of Exocets. Six that were known. Three of those six destroyed RN vessels (Sheffield, Glamorgan, Atlantic Conveyor), and as pointed out a fourth was blasted by a fluke shot from Avenger. A fifth was aboard a Super Etendard that got shot down by a British Sea Harrier before it was fired.
Mitterand may have been under fire, but there is no way Thatcher would even consider deploying nukes against Argentina. Aside from the fact the Argentines were already losing, any nuclear attacks by Britain on Argentine ships or worse, an Argentinian city, would cause a huge ruckus. South America and Africa would forever call the Brits madmen. Besides that, Britain's 1982 nuclear force was all aboard their SSBNs. How do you use an SSBN to kill a fleet? So then you have to hit a city. Hitting Buenos Aires and killing circa ten million people in the process would make Britain a global pariah. Thatcher wanted the Falklands back, but nukes were out of the question.