I do all wad punching on a conventional arbor press. It can be done on a loading press but considering how inexpensive small arbor presses are better to have a tool built for the job.

Few alterations really speed the work. Added a return spring to mine simple stop held in place by a shop made clamp. Drill chuck large enough to hold wad punches keep the tool straight. Mines mounted on a collar slipped over the tools ram held with hex screws. Turned a soft base from a kitchen cutting board, drops over the Daisy wheel preserves the punches edge.

And you don’t need threaded punches. Store bought or shop made to meet any requirement 

Boats