If the original firearm was made for smokeless powders, you can fire smokeless powders, as long as pressures are less than or equal to the cartridges of the period.
Now this assumes a whole bunch of things.
1) The firearm has not been fired with overpressure ammunition since it was built.
2) The firearm is mechanically excellent condition
3) The metals in the gun are of high quality.
The last one is going to be unproveable unless you conduct a destructive analysis of the metallurgy of the rifle. What I can say is, the metallurgy and the technology of the period, where just awful. People today have zero idea of the primitiveness of the process controls, and the inspection techniques at the turn of the last century. I encounter posters all the time that think the Kaiser had a cell phone. I don’t even know if the Kaiser had electricity. Many of the factories of the period were still using steam engines, driving a ceiling shaft, which turned leather belts, which extended down to pulleys, to run the equipment. Illumination was natural lighting, or gas lights. Which was better than nothing, but it was not a lot of light.
A local hardware store had been in the family, at the same location, since 1917. The attic is used for special item storage and I have been in the attic. The pipes for the gas lights are still in the walls and ceilings. And the rafters have real 2 X 4 studs:they measure two inches thick and four inches wide! And they look like walnut! The current owner, who worked in the store as a teenager, end of WW2 and early 50’s, remembers seeing the gas lights (had mantles) being lite from the floor with long lighters. Moderns project today’s technologies back to the past. But it was not so.
Wrought iron was purchased by reputation. Material certifications and property tests were not conducted, and I don’t know why. No one was using chemical analysis from what I read, that early wrought iron was highly variable because neither the manufacturer, or the buyer, had the technology to conduct quick metallurgical analyses. Until the open hearth process became widely available and used, steel started with wrought iron from a foundry.
This is of interest, right in the same time frame as your rifles.
The Royal Mail Ship Titanic: Did a Metallurgical Failure Cause a Night to Remember?
https://www.tms.org/pubs/journals/jom/9801/felkins-9801.html
Notice the percentages of copper and nickel in the period and modern steels. It is higher in the Titanic steel, and lower percentages in the modern. I am surprised to see any in the modern, but this is a cheap steel, so maybe the modern maker was not particularly careful about the scrap put in the kettle. Back then, steel processes could not remove non oxidizing metals, such as copper and nickel, and the stuff tended to accumulate within the steel foundry, as local scrap was put back into the kettle. These impurities, because they are uncontrolled, decrease all of the major properties unpredictably.
I cannot find the post, but somewhere I have the post from a metallurgist who conducted a materials property test on a British WW1 aircraft steel billet. He claimed it was weaker than any modern steel due to the impurities and inclusions.
And this might be of interest: in 1936, Phil Sharpe was warning shooters about early firearms:
There has been a great deal of improvement in steels, whether they be ordinary soft steels or various forms of nickel steel. No attempt with be made here to describe steels, as the subject would require and entire book. Thirty years ago, very little was known about heat treatment..
If you had a Winchester Model 1892 manufactured in 1905 and an identical model manufactured in 1935, assuming the original gun to be in perfect condition inside and out, you might place them side by side and notice absolutely no difference at firs glance. Careful study, however, will reveal that the later gun is manufactured better, with a minimum of tolerance, slap, looseness or whatever you may choose to call it. That, however, is the minor part of the of the whole thing. There will be little laboratory resemblance between the material of which the two gun are manufactured. Changes and improvements are being made constantly, and where changes in the quality of steel or the strengthening of certain parts through heat treatment are made, the factory rarely, if ever, makes any announcement. If these same Model 92 rifles were fired with a Magnum .38/40 load, it is quite possible that the earlier gun might go to pieces, while the later one would be perfectly safe. These facts must always be considered in handloading.
Complete Guide to Handloading by Philip B Sharpe. First Edition 1937, Chapter XXX, Magnum Handgun and Rifle Possibilities. Mr Sharpe was born in 1903, died 1961.
Phillip Sharpe knowledge of metallurgy is even more superficial than mine, it is obvious he knows very little about metals, metal compositions, and metallurgy. There is no doubt he has heard about enough blowups of old, vintage rifles, that he is trying to warn shooters.
So after all this gloom and doom, I cannot prove that your rifles are made from low, or high quality metals, but the technology of the period was not up to modern standards and was highly variable. Therefore, don’t push the pressures. Those cartridges, 32-20 and 38-55 were blackpowder era cartridges, and, unless you can find something from the period approving smokeless use, I would be very careful about a choice of powder. I don’t even know if you could use jacketed bullets, it might wash out the rifling.
I have used AA5744 in a 45/70 black powder era Martini Henry action, and that powder was made so that the reloader could use a smokeless propellant at blackpowder pressures.