How To Counter Bore?

[EdK]

After contemplating a lot of grinding on an old end mill, I vaguely remembered that I had bought a couple of small solid carbide boring bars off of ebay some time ago. Surprisingly I was able to find them in quick order.
Anyway, it looks like the smallest of the two might do the job. My question is whether a boring bar this small is up to the task without risk of snapping in two? The material is 1018 CRS direct from our friend Russ. Any thoughts?

Thanks,
Ed