I too live in Arizona. Where the BLM and other authorities post signs that recommend we NOT utilize our own public lands due to illegal drug runners who are armed in the desert. At Organ Pipe Natl Monument, very close to the border, park visitors are escorted by a SWAT team as they view the park. Seriously.
In the desert/woods/wherever, I suggest carry your regular carry gun. Beefed up as appropriate (magnums vs 38s etc). If you want a 22 plinker, carry that as well. If the added couple of pounds REALLY puts a damper on your outing, geez loose a couple of pounds. Or just pee before you go.
Of all the places I'd want to be armed, the wilderness is prime territory for a multitude of threats, human and otherwise. ALL of whom are likely better predators than you are. Most of whom will likely be nothing more than irritated by a 22 shot or several.
Isn't that the whole purpose of carrying a weapon? To be prepared?
Sgt Lumpy - n0eq