That link is to either a copy of or a not labeled standard Roper
Whitney hand punch.
This pattern will not take shapes other than round as both the punch
and die a loose to turn in the punch body.
So only round will work in this hand tool.
However Roper Whitney also make larger versions of this type of tool
for bench mounting.
I havnt look but can also recall different shape punches can be
used. So the punch and dies for the bench tool will be held
differently in these larger models.
Your are starting to look at production tooling. Are there any s/h
machinery dealers near you? they might just have a fly pres of say 1
to 2 tons.
small enought for the normal jewellers w/shop but much more
versatile than a larger bench type of the illustrated punch.