I've never made 300, but I pin together layers of fabric & then trace the shape onto my fabric. Then I just cut freehand with my rotary cutter pinking blade.
But, to be honest, I've never done that with circles. Typically circles fray very little because you are cutting on the bias. When fabric frays, it's the warp or the weft that comes out. With bias cuts, you don't have long sections of either that can come undone & fray. Personally, I'd just cut them with the 1/4" allowance & be done with it. When I was getting ready to needle turn them, I'd make 4 tiny snips at 12:00, 3:00, 6:00 & 9:00 and that would be enough to get the edge of the circle completely smooth.