I encourage new balisong artists to tape the blade for the first week or two. This will let you get past your fear of the blade and develope a feel for how the knife moves as well as a bit of confidence in your ability to handle it. This will temporarily put your natural fear of the blade on hold while you get a basic level of comfort with the knife.
But, I do encourage you to take the tape off as soon as you feel that bit of comfort and confidence, probably a week or two. Keep the tape handy because the first few times you go through a particularly tricky new technique, you may want to tape the blade again. This will let you concentrate on the new technique itself without worrying about the edge. When a high-wire acrobat learns a new routine, he starts off low to the ground and with a net. You can do the same thing. But, again, you want to get the tape off as soon as you think you've got the basics of this new technique down.
Why untape the blade? First, you will learn bad habits if you don't. Second, you will never loose your fear of the blade, so you will never truly become a balisong artist. Third, because you know you've developed bad habits, your fear of the blade will grow stronger and as your fear grows stronger, you'll become more dependant on the crutch of tape. But, you'll know in your head that to truly be a balisong artist, you have to do your stuff without the tape. But your fear will keep you from removing it. So, you'll give up. Worse than that, your failure at this will actually become something that will destroy your self-confidence and self-esteem in other areas of your life.
Finally, you may want to tape the blade briefly when you try out a substantially different knife. For example, if you start on the typical 4" blade, but later decide to try a 3" or 5" blade, you may want your safety net back for a day or two until you get the feel of the new blade size. This is not only for your good, but also will protect the knife from dammage while you work through the ackwardness of a new length or style.
When you take the tape off, you ARE going to get cut. If you can't accept that fact, then give up the balisong right now.
Now, let me give you some good news: I have never required a doctor's attention for a butterfly knife cut on my hand (foot, yes, but that's a different story) (hint: wear shoes when practicing). I have only been seriously cut a few times (serious being a cut that leaves a scar). The vast majority of cuts I've sustained (I call them "butterfly bites") have been very minor. A good sharp knife tends to make such nice, clean cuts that, if cared for, they heal up in less than a week. As for pain, these minor cuts from these sharp blades often don't hurt at all. Occationally, I'll be manipulating my knife and suddely become aware of blood all over the handles. I'll look around and, sure enough, there's a cut.
Proper care for the cut is this: first, keep your knives clean so that the wounds don't get contaminated. If you've used your knife to cut some packing tape on a box, clean the tape residue off the blade before returning to complicated manipulations (WD40 works very well to remove most gooey, stick type stuff including tape residue from blades). Second, for minor cuts, just apply a dab of Neosporin and then keep it bandaged. Minor cuts and scrapes of all kinds heal faster and easier when treated with a dab of Neosporin. 3M makes the best strip bandages, their "Active bandages".
Finally, while I only occationally tape the blade any more, I to have tape on my good balisongs all the time. I put a little patch of black electrical tape on the outside (with knife closed) of the handle that does not have the latch just below the slot where the latch goes in. This keeps the latch from scratching up the handle if the latch falls between the two handles during an opening (this happens a lot during reverse-grip openings). Second, I apply about three layers of black electrical tape cut into very narrow strips around the outside of the latch itself. This keeps the latch from damaging the blade if the latch falls between the handles on a closing (again, this is most common on reverse-grip closings, but can happen on any closing). Neither of these little bits of tape are there to protect the artist, so the artist will not think of them as a crutch. Neither of these bits of tape in any way interfer with the knife's movement either. They just keep your knife from getting ruined prematurely.