When a recipe calls for finely shredding an ingredient (usually a carrot for a salad or garnish or ginger), it doesn't require a four-sided box grater. Neither is it asking you to perfectly julienne.
All you have to do is cut the item on the diagonal into thin slices, a scant 1/8 inch thick. Note that when cutting the diagonal slices, the angle of your knife determines the overall length of the shreds. Then assemble the slices into several short stacks-flat side against the cutting board for stability, and use the "curled knuckles" approach to cut at 1/16 to 1/8-inch intervals for fine shreds.
The shreds will not be uniform in length, but that is fine because there's a lot of beauty in not having things always perfect. Finely shredded ingredients lend sparks of color to a dish. To have them all the same size would be awfully boring.
I recently purchase a couple of seemingly handy tools at my favorite Asian housewares shop. They were specifically made for shredding carrot and other rooty vegetables. I loved their plastic coloring and they were cheap -- 98 cents to $1.99. Here's how they fared against a knife:
The handled dragging tool make in Thailand was suppose to be great for carrots and green papaya but there were constantly times when the shreds didn't separate cleanly. Despite the convenience, it's a little awkward to firmly drag the shredded across the hard surface of a carrot. I've used similar expensive shredders made in Japan (those are about $10 and have very sharp, pointy toothed blades) and experienced the same awkwardness.
The pink one, which was textured to resemble wood, had holes that were too small. I got fine, wispy shreds more like the ones on American box graters. The interesting thing about the pink gadget was that the metallic blade was humped (curved), making the shredding process easier than a completely flat surface.
I think I'll stick with my cheap, multi-purpose Japanese vegetable knife for doing the fine shred.