Steve,

That's the kind of job I get the air powered die grinder out for. I put
in the 1/8" collet and use those itty bitty bits made for Dremel Tools.
Not knowing what the piece looks like makes it hard to tell you how to
proceed. Just make sure the piece is held firmly in something and you
can rest your hand on something while using the grinder. Kind of like a
dentist drilling a tooth. Works for me.

Ron