Is the Chiappa revolver sold as short, long, long rifle?
https://www.chiappafirearms.com/p.php?id=48
"SAA 1873-22 revolver ... Caliber: 22LR"
I suppose that is enough to create doubt about using .22 short in a Chiappa.
During my lifetime as a shooter (starting at age six in 1954) the selling point on .22 LR revolvers is that they shoot .22 Short, Long, Long Rifle, roundnose, hollowpoint, standard velocity, high velocity, interchangeably. You can't always count on other .22 LR firearms to function with shorts or longs.
Upto the 1950s there was a price difference between short, long, long rifle that made the ".22 S,L,LR" marking on a firearm an important sales point. By the mid 1960s mass production of .22 LR lowered the ammo cost until people saw no advantage to .22 Short or Long and a lot of .22 LR Only firearms took over the new gun market (like the Marlin Model 60 .22 LR only, eleven million sold so far).
.22 Short and .22 Long are almost specialty rounds today, a few made for people who prefer the round for hunting game or pests, or own older guns that are .22 Short or .22 Long only.
I am going to hazard a guess that there is no problem firing .22 Short in a Chiappa 1873-22 Revolver .22 LR cylinder. I dare opine that the caliber is listed as .22 LR because the average shooter today is not going to find much .22 Short or .22 Long on the store shelves.