Unless you want your name associated with a new cartridge there is no need to design one.
Just about every combination of case and bore size have already been tried.
Why design a 9.3 with a shortened .404 case when you can buy dies reamers and brass or loaded ammo in .375 Dakota.(There is only a .009" difference in diameter between a 9.3 and .375).
Not available at your local shop,try .375 Ruger.
Gotta have a 9.3 try 9.3x64.