OC in MO is complex as po;itical subdivisions are allowed to regulate beyond state law. If you have a CCW from any state, it is good here and i would recommend you consider that over OC as the laws in localities can and do change often and there is no requirement for them to accurately update online information they provide. The only 100% way you can OC is to review those ordinances at the city hall of each place you seek to OC. Some restrict it 100%, others restrict it to ccw holders only, and the good ones who get it do not restrict at all.
Because of that and you not knowing the lands so to speak, I do recommend CCW as the best choice, but you are a free person, do as you see fit.
In MO, no CCW is required to conceal inside a car as long as you are legally able to handle the weapon aka not a felon, so feel free to do so should you not have a ccw card.
Hope you enjoy your visit.