There is no Copal #2, but there are some odd sizes that nave been called #2.
However there was a Compur #2, as well as several odd sizes which have been confused with Compur #2. The sizes given on the SK Grimes site is, unfortunately, not the correct one.
My 1962 Compur manual lists 3 different #2's - Compur 2-X Tube 5/I, Tube 5/II and Tube 6/II. The two "5"s share a 50mm x 29 1/13 tpi mounting thread, while the "6" is 55.8mm x 20 1/13 tpi.
Both the lenses I have that are in #2 shutters are in 2-X Tube 5/II. This includes 165mm f:6.8 Angulon and 240mm f:5. Symmar. My 180mm f:4.5 Xenar is in an older shutter with slightly different threads - but if it were some years newer it would have been in a 2-X 6/II.