Neither the .45 or the .40 will qualify, legal handgun stuff pretty much starts with the 41 mag.
357 will with some loads in longer barrels, but you better have some printed ballistics from a manufacturer to back you up.
The safe bet is 41 mag or bigger, the game wardens in Wyoming that I have dealt with over the last 15 years have with one exception been great.
But rules are rules, and they are just doing their job, make it easy and uncomplicated for them.
The best shot I ever made was an accident