The iron-on banding is going to be too thin to be durable.

You can cut (or have cut) solid wood strips and glue them on the edges. A lot will depend upon the diameter of the disk, but I'm guessing they're about 12" or so. It's also important to use a wood with fairly straight grain lines. Grain runout will create weak spots.

I've made hundreds of Shaker oval boxes with bent-wood sides. For these, I soak the wood in hot water for 10-15 minutes before bending and work while hot. Hard maple would match the birch fine and bends well. When worked this way, you can bend while hot, clamp into a loop a bit smaller than your disk, then apply to your disks once cool and set.

If thin enough and diameter large enough, you can just cold bend (or laminate up two even thinner strips, glued together. I'd probably start with 1/16" (~0.062") thick wood

For a neater look, I'd taper the underside end, wrap over, then sand down the upper layer to make a scarf joint.

If you don't have a band clamp to hold while gluing, you can use tape such as masking or packing tape and work your way around the circumference.

This post was edited by bobsmyuncle on Mon, Jul 21, 14 at 10:41

That's very helpful. Thanks for the information!

Hard maple laminated like you could do.