Good news, and bad news.
The good news is, yep, your Texas CCW license is good. (Everybody's is, which is great!) MO CCW laws are outstanding, as you can carry just about everywhere that makes sense and that's not posted, and the consequences of carrying where posted is that they can ask you to leave. (If you refuse to leave, they can charge you with a misdemeanor, but at that point you're asking for it.) The CCW law is uniform across the state.
The bad news is that unlike the CCW laws, the OC laws are subject to local preemption, so they can vary by locality. Warsaw's relatively rural, so I'd bet you'd be just fine OC'ing, but that's just my .02.