I think a hole saw would be quite rough on the copper layer, you'd need one with very small teeth for such a tiny circle. You must also clamp the blank board very well to the drillpress table or you get a'very' bad finish.
How many is 'a few'? If that's less than 10 boards there is another method.
If you have access to a lathe that is. You need to clamp a 3/4" dowel into the chuck and face its end flat. Cut the boards square, a little over size and clamp them against the dowel end, one at a time, with a piece of waste ply wood and pressure from the tailstock's live centre. You can now carefully turn it round with a very good finish.
Cheaper than getting a special punch & die, which would require a punch press to use. Better finish than a hole saw - but you need a lathe :wink:
Good luck,
Klaus