The lathe tool shank size is irrelevant as long as it does not exceed the largest size it will take.
Just grind away most of the tool steel before actually grinding the cutting part.
For such a small cutter, it would be better to use a much smaller piece of HSS as a starting point – packing material below the cutting tool is far cheaper than HSS and there is no need to get the top of the cutter at the correct point, as it can easily be adjusted.
Adding a scale to your pics would help to give the scale of the item.
I will note that these safety catches appear to only prevent the trigger being pulled. Safer than nothing, but it does not prevent the mechanism discharging like an intercepting sear would.