"Is it safe to shoot modern high speed 32-20 factory loads?"
There are really no "modern high speed" loads for the .32-20. As previously stated, the high velocity .32-20 load has been extinct for many years and you are not likely to find any of that. In fact, any .32-20 ammunition is not the easiest to find in most areas, although it is still loaded and available through internet ammunition sellers and sometimes at gun shows. Reloading eliminates such problems.

You might be aware that S&W ceased manufacture of the .32-20 M&P revolver around 1929-30 after making around 145,000 of them. The Model 1905 designation was dropped by S&W just before WWI. But some collectors still use it.