My advice, candidly, is buy some more binding from StewMac or elsewhere and prepare to replace it. Fire is hot. Binding is flammable and ill-suited to brutality like shou sugi ban. If you want the full charcoal look, you're just gonna trash your binding.
But if you want the look where it's scorched, but some natural wood is also showing through - I suppose you could use a small butane torch near the edges for finer control.
I would mask the binding, and just avoid going all the way to the edge. You can then spray a black burst edge, or apply stain with a pad, to blend the more scorched surface with the unburnt edge.
That said: You could instead also fake the shou shugi ban look by attacking the top with a nylon abrasive wheel, then staining it black. You would then sand back a little with a hard block so you only knock down the high spots and leave a lot of black in the lower areas of softer grain. You still run the risk of chewing up your binding a little, depending on how well you control your tool; but at least it wouldn't be as bad as setting it on fire.
Good luck! If you follow through with your shou shugi ban plan,I'll enjoy following your process!
Bagman