Actually you can do that from the start. Just pay attention to the A that appears when you're getting near the other side. If you're fast enough, you'll jump instead of bumping into the tree.
It looks funny when you hit the tree.
But if you jump it doesn`t take you that much time to go on with walking because if you hit the tree you loose conciousness.
It took me a long time to get used to jumping off the ziplines and avoided them because they annoyed me. Once you get it down about two times, it gets really easy. The next time you're on the zipline don't press any buttons and watch when the "A" button comes up. Then try to get the timing down. It's about right before you hit the tree.
You have to have a really accurate timing though, so spamming the A button may throw you off. I know I did it a few times just to find my gal collapsing, but it could just be me being bad at pressing the A button very fast though.
Off topic...
George George, George of the jungle~ Friend to you and me~ Aaaahhhh! Watch out for that tree!
Actually, if you press the A button before the right place, it will just not work, even if you do press it on the right time. So, spamming the A won't do you any good.