I use a flat topped 45° point on a full length 1/2" square HSS toolbit. The bit is sufficiently longer than the Dickson holder to accommodate a point on both ends.
Cutting edges hollow ground using the periphery of an 8" grinding wheel and kept honed really sharp between grinds.
For smaller jobs I use a Shaviv handheld pivoting deburring blade or use a countersink in the tailstock.
If its just a teensy burr I just use the Shaviv, even on bigger jobs.
I've always felt that the fixed blade deburring tools similar to the Shaviv would be dangerous to hand hold in a lathe.
In over 20 years I've only broken one Shaviv blade in the lathe.
Clive