As described in my thread on this subject some time back, both a 3/16"-30 and a 3/16"-32 tap would thread holes that the three threads of a Luger grip screw would comfortably fit in.
The #10-32 would not go all the way in.
IMO having the correct size Whitworth tap is nice but not essential for only three threads.
From the Luger blueprints in TBLAP -
