Of course the Falklands could not - could not - have been retaken without using Aircraft carriers. The British had no choice but to use them.
Admiral Sandy Woodward made the defense of these two floating targets his main priority - and just as obviously the Argentinians made them their main targets.
They sank an aircraft-carrier sized container ship (the "Atlantic Conveyor") but never got near the real targets.
I guess the only alternative to expensive big-target carriers is to develop UCAVs that have the same/better firepower and capability as manned fighters - the carriers for those could be titchy by comparison.
The Argentinian Sub San Luis got multiple close range shots at the British Carriers, but because of a fault in their fire control system (someone cleaning contacts had switched two wires) all the torpedoes missed.
The British never came anywhere close to finding the San Luis and dropped over 100 torpedoes on assorted whales, etc. that they thought might be submarines.