If you are side milling, the arrangement with a drilling chuck is not advised – any lateral thrust will tend to loosen the cutter. This is why Clarkson type, or ER, collet chucks are used for metal removal with milling machines, other than drilling.
A mortiser only drills out surplus timber leaving the outer square cutter to slice off the timber, to form the mortise.
The usual method of converting fixed speed drives (with only a single phase supply available) is to replace with a dual voltage three phase motor with a VFD for supply and control.
Further, the bearing at the drive end of the motor is designed for limited radial thrust (in normal use a mortiser will only experience axial thrust) and would likely be inadequate for the considerable lateral forces produced while milling metals.
There are very good reasons why people spend rather more to buy a milling machine (than a wood mortiser) for machining metals. If it worked satisfactorily, most would save a lot of money by buying the cheaper machine, would they not? Same with lathes – whilst some freehand metal cutting is undertaken, the normal metal lathe cutter is operated mechanically, not freehand as is the case with much wood turning. ‘Horses for courses’ is the order of the day!