Corsair is a particular interest of mine. I must have somewhere around two dozen books on it. None of them tells the WHOLE story, and every single one of them has errors.
There are two, however, I could recommend to someone who wants a fairly complete and mostly accurate history of the airplane, illustrated with good pictues of the airplanes. The first is Motorbooks International
Warbird History F4U Corsair, by Nicholas A Veronico with John M and Donna Campbell, 1994. You can prolly find a copy either through Amazon or ABEBooks.
The second was published in England in, IIRC 2011. It's a semi-magazine format, but quite good. Dunno if they still have copies available but I got mine about a year ago. I had NO problem using their online ordering system with my US credit card. I recall it took a while to show up--4 or 5 weeks--but when it did, I thought it was well worth the wait and the price--good words, good pictures. And remember, that's from a guy who already has a shelf full of Corsair books. You can see and possibly still order it here:
http://www.aviationclassics.co.uk/news/ ... 4u-corsairSorry but I can't be as helpful on Hellcat books. I only have maybe a half-dozen on that airplane and those are mainly concerned with paint and markings and suchlike.