I cut my share of line as a surveyor for over 30 years. My favorite tool to do so was one of the SS bladed, "katana" Samurai swords.
They are sharp, lightweight, have reach, and dont tend to overtravel on the cut. With the proper cutting technique, you can usually cut a "green" 3" tree or limb in one cut with one. Ive also (unintentionally) cut through barbed wire fence unseen in the brush with it too.
If it just has to be a brush hook, you want one like Goblin shows in his link. It cuts in both directions and is a better tool for the job. We always had a couple of this type on our trucks.
Ive used the ones like that in your link too, and they work, and they, and brush hooks in general, also kind of suck. The biggest problem with them is, they tend to be heavy, slow to swing, and dont really cut very well, even when sharp. They also tend to overtravel when you swing. are hard to stop once you do, and can be dangerous to those who are near you as you cut. More so that other things anyway.
The one tool I always hated for cutting line, both to use and be around someone who was, were the machetes. They are too short, have no reach, and generally dont cut all that well, especially with things that are heavier than "leafy". Leafy stuff and people seem to be their favorite things to cut.
Ive seen a number of people cut with them over the years, and in a number of ways. With one, the blade broke about 4" back from the tip, and that piece impaled the boy behind and off to the side of the user in the leg.
Another time, one of the office engineers was out with us and was carrying one on his "upstream side" of the river we were walking across to get to an island in it. He was wearing shorts, and let the blade "dip" into the current, and it took it into his leg. Made a nasty cut too.
This is what I use.....
This is the sort of thing we used to cut through....
https://uniim1.shutterfly.com/ng/se...1/media/62908564431/medium/1190387865/enhance
