I can't give you a direct answer, because I have no experience with either the gun or the round...
That said, there is one thing that I do know:
If the pistol will properly chamber .32 Long Colt, then you can use .32 Short Colt ammunition in it.
The shorter cartridge will leave a ring of fouling in each chamber, and, after a while, you will no longer be able to stuff the longer cartridge into them until you clean the ridge of fouling out.
The cartridges you have are collectors' items, as they are no longer made.