This post examines the US and British English versions of the terms.
To start with, OK is, strictly speaking, no longer considered an abbreviation. Its origins are debatable, but a common version—and my pick—is cited by the Urban Dictionary, which claims OK was first used as a joke in a Boston newspaper in March 1839. It was:
"—an abbreviation for all correct, the joke being that neither the O nor the K was correct. Originally spelled with full stops or periods, this term outlived most similar abbreviations owing to its use in President Martin Van Buren's 1840 campaign for reelection. Because he was born in Kinderhook, New York, Van Buren was nicknamed Old Kinderhook, and the abbreviation proved eminently suitable for political slogans."
Old Kinderhook lost the election, but the term remained in popular use.
Regardless of origin, okay developed out of OK, and nowadays, both are commonly used in writing on both sides of the Atlantic. If you plan to include okaying and okayed, I would opt for okay. OKed and OKing (OK'ed and OK'ing in US English) look very clumsy. O.K. is acceptable, especially in journalism and academic texts, but it's uncommon in other writing. The version ok isn't recommended, and some experts claim it would be pronounced 'ock' in any case.
The style guides differ in UK and US English, so if you use a style manual, stick to what yours recommends. If you don't, just choose OK or okay and be consistent.
And no, I'm not going to end with a play on either word.