We make custom drill bits in finer diamond grits that can go up to a 500 grit. Let's see how that would work to add a polish.
You could drill a standard 2.5mm hole and then re-drill the hole with a customer, 2.6mm drill bit, in a 500 grit to polish it up a bit. You can also use diamond paste and a flex shaft to clean it out. Both techniques will work.
I have also heard, but never tried, to coat the hole with a clear nail polish so proceed with caution!