First of all, I assume you to be from Kansas? If not, please correct me.
Wyoming is an unrestricted open carry state. The only places you cannot carry open are those restricted by the federal government. However, the statutes used to provent carry in federal facilities are under Title 18, Part 1, Chapter 44, Section 930 - read the statutes! Pay especial attention to subsections (a) and (d)3. These parts state that lawful activitiesand incident to hunting,allow the carrying of firearms in federal facilities. If you want, contact me to discuss further, or I can send the statutes concerning carry in federal facilities.
If you pass through the Lander area on your way to Cody, let me know if you'd like to meet for a coffee - carrying open of course!