One idea is to drill a hole in a little block of wood with the drill that you will use to drill the barrel end. Then, gradually drill with increasing drill sizes, just a little bit into the hole, until it fits over barrel. If you have a caliper to measure the barrel end diameter, you can know what the final drill will be. I do it in two steps, one intermediate drill and the final one.
Then place the big hole end over barrel and drill with small drill though the other end, holding block as straight as possible. The barrel needs to be clamped in something rigid unless you have three hands.