Yes, Oman's "Nelson" is still The Biography.As to Cochrane, here are two links that should help you:
http://arthursclassicnovels.com/arthurs/adventure/tommy10.html
http://www.gutenberg.org/browse/authors/d#a5543
He is a fascinating commander and POB's "Master and Commander" is heavily based on the fight of "Speedy vs EL Gamo" (C. commanded Speedy)
If you are reading Forester and Kent,you may also like to look at Frederick Marryat http://www.gutenberg.org/browse/authors/m#a627
"Frank Mildway, Midshipman Easy" or "Peter Simple" Marryat is the first who wrote naval fiction about AoS and at one stage he served under Cochrane.
You may find it interesting that POB's "Mauritius Command" is based on the real Mauritius Campaign of 1809
As Mr Trinque wrote: The historical background of Patrick O'Brian's "The Mauritius Campaign" is the historical effort of the Royal Navy to capture the islands of Reunion and Mauritius in 1809-1810. O'Brian followed the course of the real events very closely in his novel. With one exception, he kept the historical names of the ships involved (HMS "Bombay" in the novel was actually HMS Ceylon; the name was changed to avoid confusion with an Indiaman also named Ceylon). And in most cases he used the names of the actual participants in the campaign, two exceptions being Jack Aubrey (who fills the historical role of Josias Rowley) and Lord Clonfert (who commands the same ships as the genuine Nesbit Willoughby).
(see the links)
http://hometown.aol.com/batrinque/personal2/index.htm
http://www.wargamer.com/aos/mauritius-epitaph.asp
I hope I have not spammed you too much.
Have a save weekend