What tool or technique is best for cutting circles in matte board? I am laying out a frame where I will have to cut approximately 200 aligned 35mm circles in a matte board or foam core board. I will be putting plastic coins into the holes and backing with another board (exposed foam board or something with a little give to mould to the piece) to secure the coins from sliding or rotating.
I purchased a Fiskars Circle Cutter but have discovered through testing that while the device can make the circles, it lacks the depth to cut through the whole board.  I checked to see if they sell a replacement blade with more exposed length but they do not appear to.
This then resulted in me fiddling about with an Exacto knife trying to make a clean completion cut.
If I had to do a few holes I would  accept this method, but I am somewhat nervous at the thought of repeating the process 200 times without scoring or marring the matte.
Is anyone aware of a simpler technique?
I believe a punch is probably the correct tool, however I am reluctant to invest too much for a one-off project.  I also considered using a bore saw and my hand drill but am concerned that it would just make a horrid mess of things.
A hole saw should work fine if you can find a fine tooth model. They are not as easy to find as the common coarse teeth models meant for wood. One with a thin kerf would be best.
I have also used the sharpened steel tubing trick mentioned by @fred_dot_u. An alternative to punching is pressing the sharpened tube against the board and spinning it. The spinning action makes it work like a circular knife, cutting the fibers cleanly. If you can't find a 35 mm steel tube, you can get almost as good a result by wrapping thin aluminum from a soda can around a 35 mm thick piece of plastic or wood.
To align the holes perfectly, it will help to make a template. Cut three holes in a smaller piece of board, align two of them to existing holes on your workpiece and then put your cutting / drilling tool in the third hole to keep it in correct position.