If you are nervous about using an awl by hand, get an awl blade, put it in your drill press but do not turn it on. Use a stitching wheel to mark your hole locations. Put a piece of cork board on the drill press bed, put your leather down, then use the drill to punch (not drill) your holes. Just make sure you put a slight angle to the holes to make them look right.
Also, make sure you use a good quality glue and let it dry first.
Is the above proper use? No but at least you end up with the right shape holes and they will go straight through