There's usually an event where kids can win free stuff at rodeos. It usually involves tying a ribbon to a calf's tail and the first kid to chase it down and yank the ribbon wins a free hat or something. Adults don't usually get to do this, but given your height limit and inability to grow facial hair I'm betting you can fool them all! Think of the advantage you would have!
Cheyenne is a nice town. Never been to Casper. If you decide to see Mt. Rushmore or the Black Hills let me know, I be happy to meet up with a fellow MAPer! We could go shooting if you want, I'm buying a new .270 next weekend!
Another thing I'd strongly recommend while you're in that part of the world is white water rafting. Although... you may not have the upper body strength for it.
I'm too late to give advice about the subject matter at issue, but it looks like you got good advice here. Just wanted to add: (1) hope you had fun (and post how your experience was! ); (2) Wyoming is a great state; and (3) for everyone laughing and/or shocked about drive-through liquor stores and ammunition stores, it's an anti-shoplifting and employee safety measure. When you've got a single employee watching a store in a rural area with police an hour away, a drive-through format prevents "five-finger discounts" and also allows the employee to just shut the window in case of an attempted robbery (or rape in case of a female employee). It makes perfect sense if you think about it.