I'm in Taiwan quite a bit and have asked around about the knife laws.
From what I understand, any length folder is okay as long as you're not
flashing it around and scaring people.
A machete is okay on the trails, but having a sharpened long sword is illegal.
You'll see people walking around with long swords for martial arts training, but the blades are not sharpened.
A few years back, an attempt was made to ban switch blades and balisongs,
but the law didn't pass.

However, unlike the old days, knives can no longer be sold in night markets - at least not legally.
I've brought knives in and out of Taiwan and never had a problem. Knives are
very common tools in part because of the traditional markets everywhere. Vendors use knives publicly everyday, so seeing a knife is
not too big a deal for most people.
If you buy a locally made knife that is not a U.S. brand, they are pretty cheap -say a Jaguar balisong or some folder. If you buy, for example, a CS knife that's made in Taiwan, it'll be several times what you'd pay for the same knife in the U.S.
If you don't already know this, a piece of advice - beware of the wasps/
hornets in the mountains. The vipers are dangerous, but a hive of angry wasps/hornets is deadly.
Enjoy your trip. My impression has always been that for the most part,
people in Taiwan are very helpful and generous to foreigners. It's a good
place.