Outlaw; There is no reason you cannot shoot .22 Shorts in a rifle chambered for .22 Long, or .22 LR, IF you can load them into the chamber!
A semi auto, or a 'tube fed' pump action, may take issue with their length, and jam, but, if single loaded, the have the same dimensions as the .22 LR, except for length.
Some things to consider:
(1) Price; the shorts will cost more than LR ammo, today.
(2) Accuracy; the Short has to make a big 'jump' from the case, into the rifling, no aid to accuracy, and, if the chamber is of 'sporter' dimensions (ie, over SAAMI 'Min Chamber' dimensions) the shorter rounds, not pushed up into the 'leade', will be axially 'skew to the bore centerline, causing the bullet to be distorted, some, as it 'slams' into the rifling, at the end of the 'jump'; Moreover, most 'dedicated' .22 Short rifles are rifled with a turn in 18", optimal for the 30 Gr bullet, in the Short, Where a barrel for .22 lr is usually a turn in 16, or 16 1/2, inches, to stabilise the 40 Gr bullet standard for that round; these were the same numbers Winchester used, 125 years ago, in the Winchester Single Shot (High and Low Wall) Rifles.
I've seen a bunch of 'Winder Muskets' with chambers lengthened to accomodate the .22 LR, with varying results; every factory chamber I ever measured was oversize, from SAAMI specs, which is one issue, but, 'set back', a couple of threads, and the chamber then recut, a couple of rifles have shot pretty well, in spite of a 'too slow' rifling twist, for the .22 LR
The .22 Long, hardly ever seen, except in ammo collections, is the 30 Gr bullet, loaded into a LR length case.
(3) Longevity of the arm; Shorts will not fill a LR chamber, and when fired, steadily deposit lead, and carbon, from the case mouth to the leade, in a LR chamber; this can be cleaned out, if done every shooting day, but gets much harder after several outings, and may even prevent the chambering of a lr round, if severe.
You might want to look at the Remington 'Cee-Bee's', or CCI's 'CB Longs'. as a hassle free, low noise, alternative, to Shorts, in a LR chamber.