rather more effectively lets send another four Typhoons, four GR4's and a pair of E-3's. unlike a carrier we can do that indefinately, and like a carrier it shows - unlike four Typhoons - that we are serious.
the other SA countries are willing to back Argentina (to whatever degree and however seriously) because they see the current UK force on the Islands as not being an indication of our seriousness on this issue.
regardless of the actual effectiveness and military logic of four typhoons, politically four fighters says 'meh' - and the decision to back Argentina is a political one.