I don't think it is fair to say that the SHARs were 'out of date even then'. Even now, it is a very competent little fighter and proved itself in the Falklands. I would say, though, that conventional fighters generally have a better range / weapons load, but that is one for the jet jockies to argue.
What I can say is that the Argies wouldn't have invaded if they didn't fancy their chances. Things that would have changed their minds would include: indigenous air defence of FI, a resident army brigade or greater, angle deck carriers, a very long range heavy bomber (Black Buck raids incurred an exponential Air Refuelling requirement and weren't really sustainable), sub launched TLAM, earlier indication of our ability to hit their mainland, etc etc.