Modern .22 shorts are too powerful for this gun. You would blow the latch or hinge pin, maybe both. And your hand in the process. Not to mention also destroying the gun.
The only modern ammunition you can use in them are .22 CB Caps or .22 BB Caps. They are half the size of a .22 short and contain nothing more than a bullet and primer. Little if any gunpowder is actually in them.
The only difference between the .22 CB Caps and the .22 BB Caps are the bullet. CB Caps use a conical shaped bullet and the BB Caps use a round nose bullet. Either will work.
Just make sure your bore is in shootable condition and the gun is in time and locks up properly.
I would not as the hing is not that strong.and the cylinder is poor and not made of the best metal.the 1873 french pistol I have was first to have steel in pistols and that S&W is not younger.leave it be and I am one who has fired one of those BUT it was in new condition.that is about 150yrs old.