That story about 'large carrier pilots' is probably apocryphal. As well as using USS Enterprise as an airfield (so described in a story about the adventure) our A4Gs also plonked on USS Kearsarge (described earlier in the other thread) as well as USS Ticonderoga c.1971-2 and that was that to my knowledge BUT SADLY I do not know everyfing.
Please recall that an A-4B from da USN was the first Skyhawk to arrest and catapult from HMAS Melbourne back in 1965 - so dere is dat. 'HOLY ****! he said after the catapult. No one heard what he said on the first downwind.
I've been at this humungous PDFing for a dozen years or so - using various download websites - sometimes managed by moi and then GoogieEggDrive and WunDrive sprung up so I brieved a sigh of relief to use their convoluted ever changing download good stuff. This FAAAA URL is a good start point because there are explanations about 'how to'. You cannot believe the troubles people can have downloading but some get it right because they read the instructions: (look around both sites for more PDFs/videos)
https://www.faaaa.asn.au/spazsinbad-a4g/