I have one of the C&H converted M&Ps. If you look very carefully at the front of each cylinder, you will see a concentric circle about 0.5mm out from the "hole" in the front of each chamber. What was done was to bore out the cylinder and then insert a sleeve in each chamber that brought it down to the S&W Special diameter. The barrel was often cut to around 4.5 inches and instead of being crowned, it was cut straight down. The ramp plus the sight on top of it often has a Parker-Hale marking if you look closely. The normal proof was the 3.5 tons sq in, rather than the 4 tons sq in of the 38 Special. However, as mentioned earlier in the string, the metal will definitely hold the "normal 0.38 Special" loading.
If you do not have a crowned barrel then it is worth having a gunsmith do this. It cost me all of $40 and converted a pistol that would give a 5" spread at 10 metres, to one that with the same load, gave a 2" circle at the same distance. Enjoy that old warrior. Dave_n