Here is a link to Branson's municipal code pertaining to firearms:
http://Library.municode.com/index.aspx?clientId=13699
Within, I see no distinction between OC and CC. It merely mentions the carrying of concealed firearms, and states within the ordinance that a permit is required TO CARRY in accordance with MO law. Therefore, I see no specific example where lawfulness is attributed ONLY to CC, and not OC. (Or, more specifically in order to clarify: Branson's ordinance makes carrying a firearm illegal....but exempts CCW holders from illegality. It does not specifically state MODE OF CARRY.)
The only part of Branson's ordinance that is questionable is the prohibition of "displaying in the presence of one or more people
in an angry or threatening manner .
I believe previous discussions have arrived at the meaning of, that in order to be determined illegal the "display", which could be construed as OC, must be done in an "angry or threatening manner" in order to fit the exact definition.
I don't think this has been tested in court, but I imagine it wouldn't fly as far as any DA would want to throw it as it would require him/her to rewrite the definition of "angry and threatening manner" to include holstered firearms.
I doubt the city would allow their officers to continue carrying their firearms in such an angry or threatening manner after that leap.
As always, these ruminations on the law are merely my own speculation. I am not a lawyer, so OC at your own risk. However, in my amateur opinion, I see nothing in Branson's ordinance to make OC illegal.