TexasCHLforum.com

According to http://www.handgunlaw.us" onclick="window.open(this.href);return false; and checking the Oklahoma laws, it states that that you need to inform the officer.
However, in a bit more investigation, it is similar to Texas, as when asked for ID, then you have to show.

So your question

SavageMythology wrote:Was it necessary (or simply advisable, or not advisable) for me to show my CHL to the officer in this situation?

I have to answer with, if you were in the passenger seat, did he actually ask you for ID, or while he was talking to your wife (the driver) did you open up about it?
If he asked you for ID, then YES, you needed to show the CHL.