Any suggestions for the cutter and how to mount it in the spindle?

Get a Mcmaster # 1604T13 Diamond Drag bit. This is a 1/8" diameter
shank about an inch and a quarter long, with an embedded diamond in
the tip. Very commonly used for single line drag engraving (no rotary
action necessary). It is best used though with a spring loaded holder,
of which I know some have just bored a 1/8 hole in a piece of 3/8 or
larger drill rod and incorporated a stiff spring above the bit.

grummy