I seriously question the Hunter FGA9 being a good ground attack aircraft for the 1960s Cold War environment. A 1960 ground attack Lightning would have a greater bombload, better avionics to operate in a wider range of more adverse conditions and far more survivable in higher threat scenarios.
It would arguably make a better strike aircraft, except it has half the range of the Hunter, though twice as fast. Drawing little circles on the map in Egypt or the Arabian peninsula or the Pacific/Far East shows how poor it would be for what they wanted. Can you even fly a Lightning to somewhere in the Far East even in ferry mode? Are there enough fields close enough together over that distance, never mind the number of stops? You'd probably have to crate them long distance.
Hunter was more than adequate for CAS/COIN. Lightning was far more expensive to operate, as the Kuwaitis and Saudis learned.
If you're talking about a Jaguar-like role, the Hunter still wins, but only because the Lightning can't reach anything important, and you'll never get a Lightning into an unimproved field like a Hunter or Jag possibly could. For avionics, it's just a matter of cost. If you can stick it in a Lightning, you can find room in the Hunter. Missiles, probably not, though a few export users equipped them with Sidewinders. Singapore kept theirs seemingly forever.
Also worth noting they weren't completely useless sharing air with more modern aircraft which outclassed them, as the Israelis found out.
If you need something more capable than that, you're better off waiting and spending for the Jag than repurposing the Lightning for anything other than point air defence. Hunter was far from perfect, but the main gripe (range/endurance) is far superior to the Lightning. It'd be a step backwards. Saudis dumped the Lightning for ground attack as soon as it got F-5's.
You're comparing a F-104 to an A-4. There's a reason the A-4 stuck around, too. Or all the other similar subsonic CAS/COIN attack aircraft since. SLUF, A-10, AMX, Harrier, Su-25, early MiG's, etc all stuck around or started beyond the "1960s Cold War environment."
I'm not even a big fan of the Hunter. More like a begrudged respect. Every time this topic comes up it seems crazy to me. If you want a strike aircraft in this period, they could design and develop one (as they later did with the Jag) or you can look at the Hunters you already have lying around and say, I think that'd probably do for now. I don't see how the expensive to operate, short-leg, high speed dash Lightning even enters the conversation.