My wife, brother-in-law, sister-sister-law, and I will be in Wyoming in mid July.
You can CC if you have a CCW with reciprocity for Wyoming. You can OC without a CCW. Check with the closest ranger station to find good plinking areas.
This Link is from an NGO but the links within may prove useful:
Here is the NPS page for Yellowstone's gun policy (Grand Tetons NP has the same info):
We are staying in a Cabin at Colter Bay, Lake Jackson, Grand Teton National Park. We will be hiking Yellowstone, GRTE, and Bridger-Teton National Forest.
Bear spray and a .44 magnum (or larger) is advisable as ursus horibilis roams freely:
Ursus Horibilis is a protected species; if one charges your party, make sure you use the bear spray first and your weapon second. By using the bear spray first, you may give yourself a legal defense for your self defense actions. And, of course, if the bear spray works, you won't wound or kill the bear.
Forest Service land has dual jurisdiction. 16 USC section 480 codifies Wyoming's civil and criminal jurisdiction for all National Forests including Shoshone NF. Shoshone was not regranted by Wyoming and Congress never accepted such a recession; therefore, Wyoming civil and criminal law has jurisdiction.