I have an 18" piece of 3/4" dowel with the end six inches turned down to fit the tubes (about 9mm)
Another one for 7mm --same design
This allows me to hold the 3/4" part with my right hand and the upper end with my left.
Also, when demoing this a couple weeks ago, one of the people watching was surprised I used the top of the wheels, he said he uses the bottom. IF you use the top, the wheel is spinning TOWARD you, so it is pushing the blank onto your dowel. IF you use the bottom, it is spinning away from you---trying to send the blank flying across the room. AND there is no room for your hand to hold the tip of the dowel.
Since I have started this method, I have never had a blank fly off the buffer---which used to happen at least once or twice a month. ALWAYS on my best pens, just before they were finished and they ALWAYS cracked or chipped!~!!