That makes a great deal of sense, go ahead and drill away.
If it goes wrong just say Walter told you to init?
Do you not have a vice on your pillar drill to hold it with?
Do you have a pillar drill?
Make a Heath Robinson jig with a pair of vice grips and a block of wood and drill on the lathe very carefully and slowly init?
No vice grips commonly called Mole grips?
Use a pipe wrench (stilsons), don't have one of those.
Make one with a leather belt and a stick.
They will all hold it while you drill init?