I think there could be a book on de-burring methods. I have a selection of hook type deburring tools (Noga and similar), a very lashed up version of the OP's picture which is a broken stump of a largish drill shoved into a file handle.
However, my weapon of choice for lathe work is a triangular file, about 1/2" face width, shortened, ground to a point but with the file teeth left on the back half. This was inherited from my Dad who used to in industry to make Clearview Screens for the Navy. To use:
- Internal holes – use the pointy end as a hand turning tool (no rest needed) to take off any burr.
- External shoulders – use the file teeth end to knock off the aris.
- Make sure Elfin Safety is not around.
Another good way of deburring multiple holes is a largish drill in the battery drill – you can do dozens of holes in the time it takes to type this screed.
Martin