I am also not a lawyer, so this isn't legal advice. The OSBI page you linked is talking about SDA licensing. OSBI is the Oklahoma SDA licensing authority.
I don't see a prohibition here:
https://www.oscn.net/applications/os...p?citeid=69740
As I understand it, as long as you aren't prohibited from possessing firearms or ammunition, you can carry concealed or unconcealed. There are places that you can't of course, and that goes whether you have a SDA permit or not. A lot of people are not renewing their SDA licenses due to CC. But if you do that you lose reciprocity with other states, so I maintain mine. If you never leave the state,
"legally speaking" you don't need a SDA permit anymore in Oklahoma.
Another source that alludes to CC for all:
https://oklahoma.gov/governor/newsro...stitution.html