Just an idea but what about a navalised F5 or F16. The F16 was considered for carrier ops at one piont not sure as to.the reason it wasnt pursued probably to do with the US wanting the larger more capable F14 and F18. Not to sure about the F5. Both are small, fairly agile and can carry reasonable pay loads.
The main reason the the F-16 was not pursued was at the time, was it didn't have all weather capability, a vital quality for a naval fighter.
Edit: Also the USN favored twin engine designs, for safety reasons.