When I first learned of tenkara there were no tenkara rods sold in the US. I tried both of the "shoestring" methods described above, as well as "rescuing" my old cane pole from my parents' basement (last used over 50 years earlier!). They will give you a hint of what tenkara fishing is like with a real tenkara rod, but only a hint.
The rods have evolved over hundreds of years in Japan to be very light (an 11-13' rod weighs roughly 2.5 to 3.5 ounces), capable of very effectively casting what is essentially just a 12 to 18' leader, and supple enough to protect a very light tippet. There is a definite advantage to using a rod designed for the purpose you are using it for. In this case, longer than 9' (like your existing fly rod) and designed to cast a very light line rather than a bobber and worm (like a panfish pole, or worse, cane pole).
I'm a firm believer that people should fish any way they want to fish (as long as it's legal). I also believe that if you want to try tenkara fishing, you owe it to yourself to try it with a real tenkara rod. They really aren't all that expensive, and you don't have to buy a reel and expensive fly line. There's a post in another thread by a guy who used a cane pole and short line to fish flies many years ago, gave it up and moved on, and isn't interested now - been there, done that. Only problem is, "there and that" wasn't really tenkara. If you try to do it on a shoestring you might give it up because of the limitations of the "shoestring" and never realize that the real thing just isn't the same thing at all. Having tried the cane pole route myself, I can understand his ambivalence. Not having tried a real tenkara rod, I'm not sure he can understand my passion.