There is no need to drill the entire pin, you only need to remove the head, the part that’s been peened to create an interference fit, once that’s done the pin will drive out easily.
Also, start with a smaller bit to establish center, then use a larger bit to removes the head. If you are doing this a lot invest in some machinists center drills, so much easier than a twist bit.
I understand what you’re saying now, I did that with a hand drill and then drill press as soon as I got them now use a round bit on a dremel, I was more trying to explain what you can do with minimal tools, than what I do now. I was also warning against ever trying to drill all the way through.Also, if for some bizarre reason you are trying to drill through, drill halfway thru, turn the piece over and drill from the other side, you have a much better chance of meeting in the center than hoping to drill from one side. As always, mark your centers carefully, smaller bit, make sure it’s sharp, use a cutting lubricant and go slow. A machinist vise can go a long way in keeping the knife plumb if you are careful setting it up, much better than hand held!