It is possible to cut regular, small diameter circles without buying a lens cutter. It can be done with the assistance of a Lazy Susan or cake decorating turntable.
Draw the circle of appropriate diameter on the turntable with a compass. Place the glass on top of the turntable, and position your cutter above the drawn circle. Press on the cutter with one hand and turn the glass with the other.
Steady your hand with the cutter by keeping your elbow tight against your side. This enables you to make a very good, if not perfect, circle without buying an expensive small circle cutter.
If the glass is too dark or opalescent to see the line, make a template and put it onto the glass. Cut beside the template or use the template to mark the glass. Then place the marked glass on to the turntable and cut as with transparent glass.
You will not be able to run the score by turning the glass upside down and pressing as you can with larger circles. You will need to make a number of relieving cuts to the tangent of the circle and break them away one by one. Yes, this does leave a rough edge at various places around the circle, so grozing or grinding will be necessary.