Removing copper pour

I am modifying an existing circuit board by adding an additional small PCB (2"x1"). The area I want to attach it in has a copper ground pour, and I want to remove just a small bit of the copper in order to install small eyelets for the PCB attachments and wire to the appropriate points (+V, -V, Gnd, in, out).
How can I easily and neatly remove the copper? Is there some sort of etchant that I could apply (using masking to restrict the area) to do this? I have considered just using an exacto knife and maybe some heat, but this seems less than ideal.
Any ideas?
 
For what it's worth, I was a wiring technician at a company that made test jigs for major manufacturers before I retired, and it wasn't unusual to get one back from the customer seeking revisions or upgrades. We frequently resorted to small kludge board mods using that very technique and never got any complaints. If it's done right, it doesn't look bad at all.

Mike
 
Dremel and very steady hand with a dentist type ball file or mill tip or:
1) cut through copper foil reaching epoxy below with an shatp knife to separate area to be pulled out from remaining copper.

2) scratch solder mask away so tin can stick to bare copper

3) heat a piece of that copper near one edge or corner with molten solder, it will soften adhesion (that´s why it´s easy to pull pads and tracks with careless soldering) , lift one edge or corner with knife tip.

4) once you lifted it, grab it with long nose pliers and pull, while melting the solder puddle.
Foil will be released under heat, move puddle around until foil is fully pulled out.

That´s why we expose copper first, heat transmission through molten solder is excellent and at the same time, well more localized than under a flame or hot air jet.

5) clean area with alcohol and toothbrush, then slightly polish with steel wool.