Hello,
You may be able to gain some "wiggle room" by using the Inset Function on your Cut Path. Negative inset will move the bit away from the piece (positive numbers move the bit inwards). If you are losing 1/16" around the perimeter as-is, then try an inset of -0.063" to move the bit 1/16" outwards from your Cut Path. You can apply up to 0.125" inset (positive or negative) for the cutting bit on a Cut Path.