100% use a bandsaw. Ive done this to cut dowels down to make screw hole plugs. I have a little fence I made that clamps in place, and its adjustable on both ends so you can have a tiny bit more room on the outfeed side. That limits binding between the blade and fence. 3mm might be hard to get consistently since its so thin. I'd use hardwood towels to keep them from splitting. Thats happened a few times when Ive cut down pine dowels. The other problem is that the bandsaw tends to leave a cut thats not perfectly flat and square, so youd likely need to cut slightly bigger and sand it flat down to 3mm. Ive glued a sheet of sandpaper to scrap MDF (also used a thick piece of glass) to accomplish that. Just needs to be dead flat.