There is a little tool you can cut out with a jigsaw or scroll saw that allows yout o pass the wood through the table without the fear of cutting your fingers off. It looks like a simple handle with a 1/2 inch (your choice) knotch at the bottom to grab the workpiece and help guide it through.
But never keeping you mind of the focus of the job at hand or you may cause an accident.
Here is one you can purchase, LINK
or you can make one out of scrap material lying around.