Before I had access to a large drill press I made some guide templates/blocks to help drill the string-through. It wasn't perfect, but it was as neat as I could get it and certainly better than trying to do it free-hand.

One thing that will really help is to get a long drill 2-2.5mm drill bit for the holes, as a standard length bit is really too short to use with a decently thick guide block.

But, if you really want to do a precise and neat looking string-thru I highly recommend trying to find someone with a large drill press. Local high or tech schools, community man sheds, or workshops for hire etc, look around and you may find something in your area.