Rimfire ammo such as the familiar .22 began as a black powder cartridge. By the mid-1920's, non-corrosive priming and smokeless powders had been developed and put to use. MV's with these ammos were typically no more than 1100 fps. High velocity ammo with greater MV's were developed by late 1926. By the early 1930's some HV ammo was available up to 1300 fps.
For what it's worth, in two popular and serious books from the period, Edward Crossman's Small Bore Rifle Shooting (1927) and C. S. Landis's 22 Caliber rifle Shooting (1932), there is no advice or recommendation against using HV ammo in contemporary rifles.
A good quality rifle from about any era, should handle modern High Velocity .22 ammo, just fine.
It gets a lot sketchier, when dealing with the low priced 'boy's rifles', that were so common and cheap then. They are not all created equal.
A Stevens Favorite is one example. They have a bit of a reputation for 'shooting loose', as the action pins leave a gap between the action walls and the components, allowing flex, and eventually, bending of the screws. As the entire load of firing, is carried by only the two screws, this can become a problem. One in good shape is a decent gun, one in poor shape, with about any ammo, is a hazard to the operator.
Others worth a hard look, are the various variations on a falling/rolling block type action, where the breech block has very little material actually holding the cartridge in place. Remington Model 6, for one example, some of the Stevens Little Scout models too. But lots of others like them, where you #### the hammer, then flip open a little tilting block.
Of the lightweight Stevens rifles, the 'Maynard' style lever operated break open type guns are likely to be the safest and most durable, I think.
At the end of the day, you pretty much have to judge each make and model, on it's own merits, condition, and quality. I have seen repeatedly, recommendations to stick to "Standard Velocity", 1100-ish FPS velocity ammunition, as it supposedly matches the pressures of the old ammo, which may not be absolutely correct, but... Waddya gonna do... Most of the folks around, are not reloading .22 rimfire, so you gotta pick and choose from what is available.
Right now, if I were wanting to shoot one of the sketchier models, I would gravitate hard towards the CCI Quiets as my first pick for ammo.