...and the OED claims that oll (or orl) korrect predates Old Kinderhook, who borrowed it:

From the detailed evidence provided by A. W. Read it seems clear that O.K. first appeared as a jocular alteration of the initial letters of all correct (i.e. orl korrect) in 1839, and that in 1840 it was used as an election slogan for ‘Old Kinderhook’ (see sense Ab). Thence by stages it made its way into general use. Other suggestions, e.g. that O.K. represents the Choctaw oke ‘it is’, or French au quai, or that it derives from a word in the West African language Wolof via slaves in the southern States of America, all lack any form of acceptable documentation.]

there, I've saved you the expense of buying all of those books.