I had a similar situation where instead I had a knob with 3/8-16 female thread and a hole in a tool with 10-32 female thread.  I took a 3/8 bolt and turned down the end to a projection length into the tool then threaded it at 10-32 and cut it off.  The knob not being original was less important so the new stud was installed with loctite into the knob and just enough anti-seize between the stud and the aluminum tool to prevent galvanic corrosion.