The .32 S&W Long is far too small in the Nagant and the possibility of split cases is pretty high. The same would be true in spades for the .32 Magnum, which is the same diameter as the .32 S&W.
Pressure is not a problem. Either .32 is a popgun compared to the original round. I have no idea why they made those cylinders in .32ACP, but they probably were made in Europe or somewhere that .32 S&W L was unknown.
I agree that the 7.62x25 would be a bit hot for that gun, but something like the .30 Luger should work just fine.
Jim