One problem is that what you have is NOT a khukuri, but a khukuri shaped machete...
I have one, and I have both HI and KH khukuri's, and there is NO similarity between the way they handle... The real khukuri's are almost useless for cutting light stuff because they are too heavy to swing fast... Your CS one is much better for that... BUT, the second you get to anything big enough to have any bark on it, the whole situation reverses itself... I have stopped using my GB Forest Axe for anything smaller than six inches because I can almost always cut it faster with my khukuri...
Things up to around 1.5 to 2 inches are cut with one swing, and, for me at least, a lot less difficulty, because the blade is long enough that you do not have to aim perfectly to hit the limb, and I also seem to have a lot more control...
I also can use both hands on it like a draw-knife to smooth the stump before spraying it with tar to seal it.