I agree with Roger 3/8 in surely not miniature chisel even if you have a miniature handle.
I do not think that this kind of chisel is a good choice, even if it would be done with high quality steel.
The reason is very simple and it is exactly the same thing as choosing a scale for modeling. The bigger the scale, the easier will be the construction.
The video shows a perfect example of the principle: the guy is holding the chisel with 2 fingers. He would have much more control if he could use all the 5 fingers of the hand on a bigger handle.
So what you need is a small width of steel and a big handle.