Looking at the picture, the head pattern and the shoulder look relatively small for the screw size. What are the odds that you could pick up an appropriate wood screw with a larger head, and simply reduce that head to the dimensions you need?
Mcmaster Carr is a great place to go for these. They have an excellent selection of "proper" wood screws, and when you find one you like they have very good dimensioned drawings of them, so you can determine very quickly if this would work for you or not. Bonus, if you do reduce the head, it's guaranteed to be reasonably concentric with the threads. This is NOT a given thing in the wood screw world. (Or really any threaded fastener these days...)
If you do decide to make a wood screw... I'm pretty good at charts and numbers and angles and generally sciencing things... But wood screws are tough to make. There's a HUGE amount of metal removed, by a form tool, from a very small diameter workpiece. The giant "flat" at the root of the thread is a bugger. The tool is easiest to grind (at least for me) if you find a suitable size and type of "off the shelf" screw, and use that as your tool making guide.