I can safely say I've never designed a golf club, closest bit to sporting equipment I done was some ninja throwing stars
I'm not a golfer but when you say short game do you mean on the green stuff or further like getting yourself out of the sand.
To make a golf club you are going to make some expensive tooling and use some expensive equipment. Advanced composites ie using heat and pressure to cure is not something many people have access to and if you do you will pay a lot of money for the priviledge. Before you even make a part you will spend a small fortune having moulds machined.
I would suggest you get hold of some pre-cured carbon/epoxy stock block (thick sheets of pre-cured plies) and machine the shape of club you want. If you want to tune the centre of gravity you could do this with bonded in high density metallic weights or changing the section thickness.
Attaching it to and keeping it attached to the shaft will be the hard bit. Easiest way would to do a design that involved a machined hole for the shaft to bond into or use a metallic dowel pin to join the head to the shaft.
Without a drawing or sketch it quite hard to suggest the best way of going about it.
HTH