The shape of the cylinder notches suggest that it is a smokeless-era gun.
That is correct. The shape of the cylinder locking slots says it is a Smokeless era Iver Johnson. When you remove the grips there will be a coil spring for the hammer, not a flat leaf spring, also an indication that it is a Smokeless era gun.
Around 1900 or so, Iver Johnson completely redesigned their revolvers for Smokeless powder.
This is an older Black Powder era Iver Johnson. Notice the shape of the locking slots. There is only one hard edge, the hand was what kept the cylinder from rotating backwards. Under the grips there will be a flat leaf type spring for the hammer. Also, note the little owl on the grips. Notice that he faces forward.
When Iver Johnson redesigned their revolvers for Smokeless Powder, they redesigned the lockwork so the bolt was trapped by both hard edges of the locking slots. Underneath the grips, there is a coil spring for the hammer, not a leaf spring. Along with redesigning the lockwork, Iver Johnson began using a better grade of steel at this time that could take the pressure of Smokeless powder cartridges. Note too, the little owl on the grips is now facing backwards.
The grips on your I. J. may or may not be original, so there is no little owl to help identifying it. But the shape of the cylinder locking slots says your revolver was made for Smokeless powder. It would still be wise to bring it to a gunsmith to make sure it is working properly, but if it checks out there is no reason not to fire modern Smokeless ammo in it. I am not sure if it will chamber 32 S&W Long, or only the shorter 32 S&W round, but whichever fits, you should be able to shoot modern ammo in it as long as everything is up to snuff.