The trick is how you hold the drill to work on the shaft. Point it up and trigger it with your thumb and you will have great control over both the shaft and the drill. Having the old 18 volt drill with the big battery is key since you can set it down with the shaft attached without it tipping over if you have for instance applied sanding sealer and it needs to dry a bit.
This will give people a chance to constructively criticize using a drill but they will be incorrect because doing it like this has no down side other than in their mind. When I build a new shaft I finish sand it just like this after taking it off my cnc. Way quicker and easier than chucking it up in a lathe. Especially for that final burnish. As I said I have many lathes but use a drill on shaft finishing. Especially used shafts not dead straight The wobble will be shock absorbed by your wrist holding the drill and you can work the shaft without noticing the runout. The shaft in my video is slightly warped.
Here is another thing I have learned when dealing with bare shaft wood either new or recleaned. You can take some 2000 grit sandpaper and apply liberally minwax paste wax to it and use it for your final finish and you get the affect of wet sanding without raising the grain of the wood. And you can work it all the way to the joint and it will not hurt the finish on the shaft down there other than to polish it back up. Follow that up with a burnish with paper towels creating a bit of heat and you will have a very nice durable shaft that feels like glass. I now prefer this wax over renaissance.