Hi Munk,
I'll have to respectfully disagree with "wrong." The regulation said, "weapon." Now I happen to agree with you that this definitely covers firearms, but if you ask most of the people who are enforcing it how they define "weapon," you often get an "ummmmmm" and a blank look. Given that the definition of weapon may be discretionary, an overzealous ranger may call a khukuri a weapon. Hence, you need to have a reason to have it that has nothing to do with self defense.
I work for a private conservancy with an almost identical weapons policy, and quite honestly, if I saw a hiker with a khukuri, I'd call them on it and call the rangers. The only danger out here are bison and rattlesnakes, and if you're close enough to use a khukuri on a bison, you're already in way too much trouble to chop your way out. Rattlesnakes are to be avoided, not killed. Otherwise, you can't harvest wood here for a campfire (due to low supplies and high fire risk), so the major reason for a hiker to carry a khukuri would be to use it on someone else--it's a weapon, in other words. When I use my Ganga to cut things as part of my job, I make sure that everyone knows it's specifically designed as a wood cutter, and rarely let it out of my possession and never out of my sight.
Also, ALWAYS check local fire conditions. If it's code red, they may declare "no campfires."
As for cougar defense with a khuk...Are you throwing it at them? I've always preferred a long hiking staff, because a cougar's much faster than I am at close quarters, and I'd rather use a long staff and thrown stones to keep them at a distance. And yes, I've hiked at dusk in cougar country many, many times. If I get nervous, I carry said long stick over my shoulder, because cougars tend to attack by jumping you from behind and go for your neck, and the stick makes that attack much more complicated. A khukuri's not a great defense under such conditions.
If you're that nervous about cougars, I'd suggest getting one of the Cold Steel Bushman knives, as they make decent spear heads, and make a spear shaft/walking stick to go with it. Carry the spear shaft as a hiking staff, and the knife on your belt as a tool. If you get nervous about big cats, put the knife on the staff, and you have a pretty good spear.