First alternative: Don't do it!............drill and file is the way to go, I've never understood the burning on thing, it takes forever and you're always prone to push too hard, thus splitting the handle........and what's the advantage of this method supposed to be, anyway?
If you mark the (roughly triangular) shape of the tang on the outside of the workpiece, stand it in the vice and drill the two sides almost to their apex; then drill the center hole and use whatever tools you have or can make to clear the excess wood from the hole...........just plug away 'till you've got the right-size hole...............don't worry about the hole being a little on the large size, a good 2 part epoxy will probably work better like this anyway!
Second alternative: Treat it as a full tang, carve the relief for the stick tang equally from both sides then glue together with or without pins lanyard tubes and even liners................It's not difficult to make this join nigh-on invisible with a little care.
I use a carpenter's handbrace with an extra long wood-bit for all my drilling, and just go at it gently..........hope this helps,......................................atb mac